| 
ref-2-id-99
 | 
exist {MissingArg} indeed {MissingArg}
 | 
| 
ref-2-id-102
 | 
{MissingArg} imply {MissingArg}
 | 
| 
ref-0-id-0
 | 
kvanti
 | 
| 
ref-0-id-1
 | 
lemma uniqueMember
 | 
| 
ref-0-id-2
 | 
lemma uniqueMember(Type)
 | 
| 
ref-0-id-3
 | 
lemma sameSeries
 | 
| 
ref-0-id-4
 | 
lemma a4
 | 
| 
ref-0-id-5
 | 
lemma sameMember
 | 
| 
ref-0-id-6
 | 
1rule Qclosed(Addition)
 | 
| 
ref-0-id-7
 | 
1rule Qclosed(Multiplication)
 | 
| 
ref-0-id-8
 | 
1rule fromCartProd(1)
 | 
| 
ref-0-id-9
 | 
1rule fromCartProd(2)
 | 
| 
ref-0-id-10
 | 
constantRationalSeries( {MissingArg} )
 | 
| 
ref-0-id-11
 | 
cartProd( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-12
 | 
P( {MissingArg} )
 | 
| 
ref-0-id-13
 | 
binaryUnion( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-14
 | 
setOfRationalSeries
 | 
| 
ref-0-id-15
 | 
isSubset( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-16
 | 
(p {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-17
 | 
(s {MissingArg} )
 | 
| 
ref-0-id-18
 | 
cdots
 | 
| 
ref-0-id-19
 | 
object-var
 | 
| 
ref-0-id-20
 | 
ex-var
 | 
| 
ref-0-id-21
 | 
ph-var
 | 
| 
ref-0-id-22
 | 
vaerdi
 | 
| 
ref-0-id-23
 | 
variabel
 | 
| 
ref-0-id-24
 | 
op {MissingArg} end op
 | 
| 
ref-0-id-25
 | 
op2 {MissingArg} comma {MissingArg} end op2
 | 
| 
ref-0-id-26
 | 
define-equal {MissingArg} comma {MissingArg} end equal
 | 
| 
ref-0-id-27
 | 
contains-empty {MissingArg} end empty
 | 
| 
ref-0-id-28
 | 
Nat( {MissingArg} )
 | 
| 
ref-0-id-29
 | 
1deduction {MissingArg} conclude {MissingArg} end 1deduction
 | 
| 
ref-0-id-30
 | 
1deduction zero {MissingArg} conclude {MissingArg} end 1deduction
 | 
| 
ref-0-id-31
 | 
1deduction side {MissingArg} conclude {MissingArg} condition {MissingArg} end 1deduction
 | 
| 
ref-0-id-32
 | 
1deduction one {MissingArg} conclude {MissingArg} condition {MissingArg} end 1deduction
 | 
| 
ref-0-id-33
 | 
1deduction two {MissingArg} conclude {MissingArg} condition {MissingArg} end 1deduction
 | 
| 
ref-0-id-34
 | 
1deduction three {MissingArg} conclude {MissingArg} condition {MissingArg} bound {MissingArg} end 1deduction
 | 
| 
ref-0-id-35
 | 
1deduction four {MissingArg} conclude {MissingArg} condition {MissingArg} bound {MissingArg} end 1deduction
 | 
| 
ref-0-id-36
 | 
1deduction four star {MissingArg} conclude {MissingArg} condition {MissingArg} bound {MissingArg} end 1deduction
 | 
| 
ref-0-id-37
 | 
1deduction five {MissingArg} condition {MissingArg} bound {MissingArg} end 1deduction
 | 
| 
ref-0-id-38
 | 
1deduction six {MissingArg} conclude {MissingArg} exception {MissingArg} bound {MissingArg} end 1deduction
 | 
| 
ref-0-id-39
 | 
1deduction six star {MissingArg} conclude {MissingArg} exception {MissingArg} bound {MissingArg} end 1deduction
 | 
| 
ref-0-id-40
 | 
1deduction seven {MissingArg} end 1deduction
 | 
| 
ref-0-id-41
 | 
1deduction eight {MissingArg} bound {MissingArg} end 1deduction
 | 
| 
ref-0-id-42
 | 
1deduction eight star {MissingArg} bound {MissingArg} end 1deduction
 | 
| 
ref-0-id-43
 | 
ex1
 | 
| 
ref-0-id-44
 | 
ex2
 | 
| 
ref-0-id-45
 | 
ex3
 | 
| 
ref-0-id-46
 | 
ex10
 | 
| 
ref-0-id-47
 | 
ex20
 | 
| 
ref-0-id-48
 | 
existential var {MissingArg} end var
 | 
| 
ref-0-id-49
 | 
{MissingArg} is existential var
 | 
| 
ref-0-id-50
 | 
exist-sub {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-51
 | 
exist-sub0 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-52
 | 
exist-sub1 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-53
 | 
exist-sub* {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-54
 | 
ph1
 | 
| 
ref-0-id-55
 | 
ph2
 | 
| 
ref-0-id-56
 | 
ph3
 | 
| 
ref-0-id-57
 | 
placeholder-var {MissingArg} end var
 | 
| 
ref-0-id-58
 | 
{MissingArg} is placeholder-var
 | 
| 
ref-0-id-59
 | 
ph-sub {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-60
 | 
ph-sub0 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-61
 | 
ph-sub1 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-62
 | 
ph-sub* {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-63
 | 
meta-sub {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-64
 | 
meta-sub1 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-65
 | 
meta-sub* {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub
 | 
| 
ref-0-id-66
 | 
var big set
 | 
| 
ref-0-id-67
 | 
object big set
 | 
| 
ref-0-id-68
 | 
meta big set
 | 
| 
ref-0-id-69
 | 
zermelo empty set
 | 
| 
ref-0-id-70
 | 
system Q
 | 
| 
ref-0-id-71
 | 
1rule mp
 | 
| 
ref-0-id-72
 | 
1rule gen
 | 
| 
ref-0-id-73
 | 
1rule repetition
 | 
| 
ref-0-id-74
 | 
1rule ad absurdum
 | 
| 
ref-0-id-75
 | 
1rule deduction
 | 
| 
ref-0-id-76
 | 
1rule exist intro
 | 
| 
ref-0-id-77
 | 
axiom extensionality
 | 
| 
ref-0-id-78
 | 
axiom empty set
 | 
| 
ref-0-id-79
 | 
axiom pair definition
 | 
| 
ref-0-id-80
 | 
axiom union definition
 | 
| 
ref-0-id-81
 | 
axiom power definition
 | 
| 
ref-0-id-82
 | 
axiom separation definition
 | 
| 
ref-0-id-83
 | 
prop lemma add double neg
 | 
| 
ref-0-id-84
 | 
prop lemma remove double neg
 | 
| 
ref-0-id-85
 | 
prop lemma and commutativity
 | 
| 
ref-0-id-86
 | 
prop lemma auto imply
 | 
| 
ref-0-id-87
 | 
prop lemma contrapositive
 | 
| 
ref-0-id-88
 | 
prop lemma first conjunct
 | 
| 
ref-0-id-89
 | 
prop lemma second conjunct
 | 
| 
ref-0-id-90
 | 
prop lemma from contradiction
 | 
| 
ref-0-id-91
 | 
prop lemma from disjuncts
 | 
| 
ref-0-id-92
 | 
prop lemma iff commutativity
 | 
| 
ref-0-id-93
 | 
prop lemma iff first
 | 
| 
ref-0-id-94
 | 
prop lemma iff second
 | 
| 
ref-0-id-95
 | 
prop lemma imply transitivity
 | 
| 
ref-0-id-96
 | 
prop lemma join conjuncts
 | 
| 
ref-0-id-97
 | 
prop lemma mp2
 | 
| 
ref-0-id-98
 | 
prop lemma mp3
 | 
| 
ref-0-id-99
 | 
prop lemma mp4
 | 
| 
ref-0-id-100
 | 
prop lemma mp5
 | 
| 
ref-0-id-101
 | 
prop lemma mt
 | 
| 
ref-0-id-102
 | 
prop lemma negative mt
 | 
| 
ref-0-id-103
 | 
prop lemma technicality
 | 
| 
ref-0-id-104
 | 
prop lemma weakening
 | 
| 
ref-0-id-105
 | 
prop lemma weaken or first
 | 
| 
ref-0-id-106
 | 
prop lemma weaken or second
 | 
| 
ref-0-id-107
 | 
lemma formula2pair
 | 
| 
ref-0-id-108
 | 
lemma pair2formula
 | 
| 
ref-0-id-109
 | 
lemma formula2union
 | 
| 
ref-0-id-110
 | 
lemma union2formula
 | 
| 
ref-0-id-111
 | 
lemma formula2separation
 | 
| 
ref-0-id-112
 | 
lemma separation2formula
 | 
| 
ref-0-id-113
 | 
lemma formula2power
 | 
| 
ref-0-id-114
 | 
lemma subset in power set
 | 
| 
ref-0-id-115
 | 
lemma power set is subset0
 | 
| 
ref-0-id-116
 | 
lemma power set is subset
 | 
| 
ref-0-id-117
 | 
lemma power set is subset0-switch
 | 
| 
ref-0-id-118
 | 
lemma power set is subset-switch
 | 
| 
ref-0-id-119
 | 
lemma set equality suff condition
 | 
| 
ref-0-id-120
 | 
lemma set equality suff condition(t)0
 | 
| 
ref-0-id-121
 | 
lemma set equality suff condition(t)
 | 
| 
ref-0-id-122
 | 
lemma set equality skip quantifier
 | 
| 
ref-0-id-123
 | 
lemma set equality nec condition
 | 
| 
ref-0-id-124
 | 
lemma reflexivity0
 | 
| 
ref-0-id-125
 | 
lemma reflexivity
 | 
| 
ref-0-id-126
 | 
lemma symmetry0
 | 
| 
ref-0-id-127
 | 
lemma symmetry
 | 
| 
ref-0-id-128
 | 
lemma transitivity0
 | 
| 
ref-0-id-129
 | 
lemma transitivity
 | 
| 
ref-0-id-130
 | 
lemma er is reflexive
 | 
| 
ref-0-id-131
 | 
lemma er is symmetric
 | 
| 
ref-0-id-132
 | 
lemma er is transitive
 | 
| 
ref-0-id-133
 | 
lemma empty set is subset
 | 
| 
ref-0-id-134
 | 
lemma member not empty0
 | 
| 
ref-0-id-135
 | 
lemma member not empty
 | 
| 
ref-0-id-136
 | 
lemma unique empty set0
 | 
| 
ref-0-id-137
 | 
lemma unique empty set
 | 
| 
ref-0-id-138
 | 
lemma ==Reflexivity
 | 
| 
ref-0-id-139
 | 
lemma ==Symmetry
 | 
| 
ref-0-id-140
 | 
lemma ==Transitivity0
 | 
| 
ref-0-id-141
 | 
lemma ==Transitivity
 | 
| 
ref-0-id-142
 | 
lemma transfer ~is0
 | 
| 
ref-0-id-143
 | 
lemma transfer ~is
 | 
| 
ref-0-id-144
 | 
lemma pair subset0
 | 
| 
ref-0-id-145
 | 
lemma pair subset1
 | 
| 
ref-0-id-146
 | 
lemma pair subset
 | 
| 
ref-0-id-147
 | 
lemma same pair
 | 
| 
ref-0-id-148
 | 
lemma same singleton
 | 
| 
ref-0-id-149
 | 
lemma union subset
 | 
| 
ref-0-id-150
 | 
lemma same union
 | 
| 
ref-0-id-151
 | 
lemma separation subset
 | 
| 
ref-0-id-152
 | 
lemma same separation
 | 
| 
ref-0-id-153
 | 
lemma same binary union
 | 
| 
ref-0-id-154
 | 
lemma intersection subset
 | 
| 
ref-0-id-155
 | 
lemma same intersection
 | 
| 
ref-0-id-156
 | 
lemma auto member
 | 
| 
ref-0-id-157
 | 
lemma eq-system not empty0
 | 
| 
ref-0-id-158
 | 
lemma eq-system not empty
 | 
| 
ref-0-id-159
 | 
lemma eq subset0
 | 
| 
ref-0-id-160
 | 
lemma eq subset
 | 
| 
ref-0-id-161
 | 
lemma equivalence nec condition0
 | 
| 
ref-0-id-162
 | 
lemma equivalence nec condition
 | 
| 
ref-0-id-163
 | 
lemma none-equivalence nec condition0
 | 
| 
ref-0-id-164
 | 
lemma none-equivalence nec condition1
 | 
| 
ref-0-id-165
 | 
lemma none-equivalence nec condition
 | 
| 
ref-0-id-166
 | 
lemma equivalence class is subset
 | 
| 
ref-0-id-167
 | 
lemma equivalence classes are disjoint
 | 
| 
ref-0-id-168
 | 
lemma all disjoint
 | 
| 
ref-0-id-169
 | 
lemma all disjoint-imply
 | 
| 
ref-0-id-170
 | 
lemma bs subset union(bs/r)
 | 
| 
ref-0-id-171
 | 
lemma union(bs/r) subset bs
 | 
| 
ref-0-id-172
 | 
lemma union(bs/r) is bs
 | 
| 
ref-0-id-173
 | 
theorem eq-system is partition
 | 
| 
ref-0-id-174
 | 
var x1
 | 
| 
ref-0-id-175
 | 
var x2
 | 
| 
ref-0-id-176
 | 
var y1
 | 
| 
ref-0-id-177
 | 
var y2
 | 
| 
ref-0-id-178
 | 
var v1
 | 
| 
ref-0-id-179
 | 
var v2
 | 
| 
ref-0-id-180
 | 
var v3
 | 
| 
ref-0-id-181
 | 
var v4
 | 
| 
ref-0-id-182
 | 
var v2n
 | 
| 
ref-0-id-183
 | 
var m1
 | 
| 
ref-0-id-184
 | 
var m2
 | 
| 
ref-0-id-185
 | 
var n1
 | 
| 
ref-0-id-186
 | 
var n2
 | 
| 
ref-0-id-187
 | 
var n3
 | 
| 
ref-0-id-188
 | 
var ep
 | 
| 
ref-0-id-189
 | 
var ep1
 | 
| 
ref-0-id-190
 | 
var ep2
 | 
| 
ref-0-id-191
 | 
var fep
 | 
| 
ref-0-id-192
 | 
var fx
 | 
| 
ref-0-id-193
 | 
var fy
 | 
| 
ref-0-id-194
 | 
var fz
 | 
| 
ref-0-id-195
 | 
var fu
 | 
| 
ref-0-id-196
 | 
var fv
 | 
| 
ref-0-id-197
 | 
var fw
 | 
| 
ref-0-id-198
 | 
var rx
 | 
| 
ref-0-id-199
 | 
var ry
 | 
| 
ref-0-id-200
 | 
var rz
 | 
| 
ref-0-id-201
 | 
var ru
 | 
| 
ref-0-id-202
 | 
var sx
 | 
| 
ref-0-id-203
 | 
var sx1
 | 
| 
ref-0-id-204
 | 
var sy
 | 
| 
ref-0-id-205
 | 
var sy1
 | 
| 
ref-0-id-206
 | 
var sz
 | 
| 
ref-0-id-207
 | 
var sz1
 | 
| 
ref-0-id-208
 | 
var su
 | 
| 
ref-0-id-209
 | 
var su1
 | 
| 
ref-0-id-210
 | 
var fxs
 | 
| 
ref-0-id-211
 | 
var fys
 | 
| 
ref-0-id-212
 | 
var crs1
 | 
| 
ref-0-id-213
 | 
var f1
 | 
| 
ref-0-id-214
 | 
var f2
 | 
| 
ref-0-id-215
 | 
var f3
 | 
| 
ref-0-id-216
 | 
var f4
 | 
| 
ref-0-id-217
 | 
var op1
 | 
| 
ref-0-id-218
 | 
var op2
 | 
| 
ref-0-id-219
 | 
var r1
 | 
| 
ref-0-id-220
 | 
var s1
 | 
| 
ref-0-id-221
 | 
var s2
 | 
| 
ref-0-id-222
 | 
meta x1
 | 
| 
ref-0-id-223
 | 
meta x2
 | 
| 
ref-0-id-224
 | 
meta y1
 | 
| 
ref-0-id-225
 | 
meta y2
 | 
| 
ref-0-id-226
 | 
meta v1
 | 
| 
ref-0-id-227
 | 
meta v2
 | 
| 
ref-0-id-228
 | 
meta v3
 | 
| 
ref-0-id-229
 | 
meta v4
 | 
| 
ref-0-id-230
 | 
meta v2n
 | 
| 
ref-0-id-231
 | 
meta m1
 | 
| 
ref-0-id-232
 | 
meta m2
 | 
| 
ref-0-id-233
 | 
meta n1
 | 
| 
ref-0-id-234
 | 
meta n2
 | 
| 
ref-0-id-235
 | 
meta n3
 | 
| 
ref-0-id-236
 | 
meta ep
 | 
| 
ref-0-id-237
 | 
meta ep1
 | 
| 
ref-0-id-238
 | 
meta ep2
 | 
| 
ref-0-id-239
 | 
meta fx
 | 
| 
ref-0-id-240
 | 
meta fy
 | 
| 
ref-0-id-241
 | 
meta fz
 | 
| 
ref-0-id-242
 | 
meta fu
 | 
| 
ref-0-id-243
 | 
meta fv
 | 
| 
ref-0-id-244
 | 
meta fw
 | 
| 
ref-0-id-245
 | 
meta fep
 | 
| 
ref-0-id-246
 | 
meta rx
 | 
| 
ref-0-id-247
 | 
meta ry
 | 
| 
ref-0-id-248
 | 
meta rz
 | 
| 
ref-0-id-249
 | 
meta ru
 | 
| 
ref-0-id-250
 | 
meta sx
 | 
| 
ref-0-id-251
 | 
meta sx1
 | 
| 
ref-0-id-252
 | 
meta sy
 | 
| 
ref-0-id-253
 | 
meta sy1
 | 
| 
ref-0-id-254
 | 
meta sz
 | 
| 
ref-0-id-255
 | 
meta sz1
 | 
| 
ref-0-id-256
 | 
meta su
 | 
| 
ref-0-id-257
 | 
meta su1
 | 
| 
ref-0-id-258
 | 
meta fxs
 | 
| 
ref-0-id-259
 | 
meta fys
 | 
| 
ref-0-id-260
 | 
meta f1
 | 
| 
ref-0-id-261
 | 
meta f2
 | 
| 
ref-0-id-262
 | 
meta f3
 | 
| 
ref-0-id-263
 | 
meta f4
 | 
| 
ref-0-id-264
 | 
meta op1
 | 
| 
ref-0-id-265
 | 
meta op2
 | 
| 
ref-0-id-266
 | 
meta r1
 | 
| 
ref-0-id-267
 | 
meta s1
 | 
| 
ref-0-id-268
 | 
meta s2
 | 
| 
ref-0-id-269
 | 
object ep
 | 
| 
ref-0-id-270
 | 
object crs1
 | 
| 
ref-0-id-271
 | 
object f1
 | 
| 
ref-0-id-272
 | 
object f2
 | 
| 
ref-0-id-273
 | 
object f3
 | 
| 
ref-0-id-274
 | 
object f4
 | 
| 
ref-0-id-275
 | 
object n1
 | 
| 
ref-0-id-276
 | 
object n2
 | 
| 
ref-0-id-277
 | 
object op1
 | 
| 
ref-0-id-278
 | 
object op2
 | 
| 
ref-0-id-279
 | 
object r1
 | 
| 
ref-0-id-280
 | 
object s1
 | 
| 
ref-0-id-281
 | 
object s2
 | 
| 
ref-0-id-282
 | 
ph4
 | 
| 
ref-0-id-283
 | 
ph5
 | 
| 
ref-0-id-284
 | 
ph6
 | 
| 
ref-0-id-285
 | 
NAT
 | 
| 
ref-0-id-286
 | 
RATIONAL_SERIES
 | 
| 
ref-0-id-287
 | 
SERIES
 | 
| 
ref-0-id-288
 | 
setOfReals
 | 
| 
ref-0-id-289
 | 
setOfFxs
 | 
| 
ref-0-id-290
 | 
N
 | 
| 
ref-0-id-291
 | 
Q
 | 
| 
ref-0-id-292
 | 
X
 | 
| 
ref-0-id-293
 | 
xs
 | 
| 
ref-0-id-294
 | 
xsF
 | 
| 
ref-0-id-295
 | 
ysF
 | 
| 
ref-0-id-296
 | 
us
 | 
| 
ref-0-id-297
 | 
usF
 | 
| 
ref-0-id-298
 | 
0
 | 
| 
ref-0-id-299
 | 
1
 | 
| 
ref-0-id-300
 | 
(-1)
 | 
| 
ref-0-id-301
 | 
2
 | 
| 
ref-0-id-302
 | 
3
 | 
| 
ref-0-id-303
 | 
1/2
 | 
| 
ref-0-id-304
 | 
1/3
 | 
| 
ref-0-id-305
 | 
2/3
 | 
| 
ref-0-id-306
 | 
0f
 | 
| 
ref-0-id-307
 | 
1f
 | 
| 
ref-0-id-308
 | 
00
 | 
| 
ref-0-id-309
 | 
01
 | 
| 
ref-0-id-310
 | 
(--01)
 | 
| 
ref-0-id-311
 | 
02
 | 
| 
ref-0-id-312
 | 
01//02
 | 
| 
ref-0-id-313
 | 
lemma plusAssociativity(R)
 | 
| 
ref-0-id-314
 | 
lemma plusAssociativity(R)XX
 | 
| 
ref-0-id-315
 | 
lemma plus0(R)
 | 
| 
ref-0-id-316
 | 
lemma negative(R)
 | 
| 
ref-0-id-317
 | 
lemma times1(R)
 | 
| 
ref-0-id-318
 | 
lemma lessAddition(R)
 | 
| 
ref-0-id-319
 | 
lemma plusCommutativity(R)
 | 
| 
ref-0-id-320
 | 
lemma leqAntisymmetry(R)
 | 
| 
ref-0-id-321
 | 
lemma leqTransitivity(R)
 | 
| 
ref-0-id-322
 | 
lemma leqAddition(R)
 | 
| 
ref-0-id-323
 | 
lemma distribution(R)
 | 
| 
ref-0-id-324
 | 
axiom a4
 | 
| 
ref-0-id-325
 | 
axiom induction
 | 
| 
ref-0-id-326
 | 
axiom equality
 | 
| 
ref-0-id-327
 | 
axiom eqLeq
 | 
| 
ref-0-id-328
 | 
axiom eqAddition
 | 
| 
ref-0-id-329
 | 
axiom eqMultiplication
 | 
| 
ref-0-id-330
 | 
axiom QisClosed(reciprocal)
 | 
| 
ref-0-id-331
 | 
lemma QisClosed(reciprocal)
 | 
| 
ref-0-id-332
 | 
axiom QisClosed(negative)
 | 
| 
ref-0-id-333
 | 
lemma QisClosed(negative)
 | 
| 
ref-0-id-334
 | 
axiom leqReflexivity
 | 
| 
ref-0-id-335
 | 
axiom leqAntisymmetry
 | 
| 
ref-0-id-336
 | 
axiom leqTransitivity
 | 
| 
ref-0-id-337
 | 
axiom leqTotality
 | 
| 
ref-0-id-338
 | 
axiom leqAddition
 | 
| 
ref-0-id-339
 | 
axiom leqMultiplication
 | 
| 
ref-0-id-340
 | 
axiom plusAssociativity
 | 
| 
ref-0-id-341
 | 
axiom plusCommutativity
 | 
| 
ref-0-id-342
 | 
axiom negative
 | 
| 
ref-0-id-343
 | 
axiom plus0
 | 
| 
ref-0-id-344
 | 
axiom timesAssociativity
 | 
| 
ref-0-id-345
 | 
axiom timesCommutativity
 | 
| 
ref-0-id-346
 | 
axiom reciprocal
 | 
| 
ref-0-id-347
 | 
axiom times1
 | 
| 
ref-0-id-348
 | 
axiom distribution
 | 
| 
ref-0-id-349
 | 
axiom 0not1
 | 
| 
ref-0-id-350
 | 
lemma eqLeq(R)
 | 
| 
ref-0-id-351
 | 
lemma timesAssociativity(R)
 | 
| 
ref-0-id-352
 | 
lemma timesCommutativity(R)
 | 
| 
ref-0-id-353
 | 
1rule adhoc sameR
 | 
| 
ref-0-id-354
 | 
lemma separation2formula(1)
 | 
| 
ref-0-id-355
 | 
lemma separation2formula(2)
 | 
| 
ref-0-id-356
 | 
axiom cauchy
 | 
| 
ref-0-id-357
 | 
axiom plusF
 | 
| 
ref-0-id-358
 | 
axiom reciprocalF
 | 
| 
ref-0-id-359
 | 
1rule from==
 | 
| 
ref-0-id-360
 | 
1rule to==
 | 
| 
ref-0-id-361
 | 
1rule fromInR
 | 
| 
ref-0-id-362
 | 
lemma plusR(Sym)
 | 
| 
ref-0-id-363
 | 
axiom reciprocalR
 | 
| 
ref-0-id-364
 | 
1rule lessMinus1(N)
 | 
| 
ref-0-id-365
 | 
axiom nonnegative(N)
 | 
| 
ref-0-id-366
 | 
axiom US0
 | 
| 
ref-0-id-367
 | 
1rule nextXS(upperBound)
 | 
| 
ref-0-id-368
 | 
1rule nextXS(noUpperBound)
 | 
| 
ref-0-id-369
 | 
1rule nextUS(upperBound)
 | 
| 
ref-0-id-370
 | 
1rule nextUS(noUpperBound)
 | 
| 
ref-0-id-371
 | 
1rule expZero
 | 
| 
ref-0-id-372
 | 
1rule expPositive
 | 
| 
ref-0-id-373
 | 
1rule expZero(R)
 | 
| 
ref-0-id-374
 | 
1rule expPositive(R)
 | 
| 
ref-0-id-375
 | 
1rule base(1/2)Sum zero
 | 
| 
ref-0-id-376
 | 
1rule base(1/2)Sum positive
 | 
| 
ref-0-id-377
 | 
1rule UStelescope zero
 | 
| 
ref-0-id-378
 | 
1rule UStelescope positive
 | 
| 
ref-0-id-379
 | 
1rule adhoc eqAddition(R)
 | 
| 
ref-0-id-380
 | 
1rule fromLimit
 | 
| 
ref-0-id-381
 | 
1rule toUpperBound
 | 
| 
ref-0-id-382
 | 
1rule fromUpperBound
 | 
| 
ref-0-id-383
 | 
axiom USisUpperBound
 | 
| 
ref-0-id-384
 | 
axiom 0not1(R)
 | 
| 
ref-0-id-385
 | 
1rule expUnbounded
 | 
| 
ref-0-id-386
 | 
1rule fromLeq(Advanced)(N)
 | 
| 
ref-0-id-387
 | 
1rule fromLeastUpperBound
 | 
| 
ref-0-id-388
 | 
1rule toLeastUpperBound
 | 
| 
ref-0-id-389
 | 
axiom XSisNotUpperBound
 | 
| 
ref-0-id-390
 | 
axiom ysFGreater
 | 
| 
ref-0-id-391
 | 
axiom ysFLess
 | 
| 
ref-0-id-392
 | 
1rule smallInverse
 | 
| 
ref-0-id-393
 | 
axiom natType
 | 
| 
ref-0-id-394
 | 
axiom rationalType
 | 
| 
ref-0-id-395
 | 
axiom seriesType
 | 
| 
ref-0-id-396
 | 
axiom max
 | 
| 
ref-0-id-397
 | 
axiom numerical
 | 
| 
ref-0-id-398
 | 
axiom numericalF
 | 
| 
ref-0-id-399
 | 
axiom memberOfSeries
 | 
| 
ref-0-id-400
 | 
prop lemma doubly conditioned join conjuncts
 | 
| 
ref-0-id-401
 | 
prop lemma imply negation
 | 
| 
ref-0-id-402
 | 
prop lemma tertium non datur
 | 
| 
ref-0-id-403
 | 
prop lemma from negated imply
 | 
| 
ref-0-id-404
 | 
prop lemma to negated imply
 | 
| 
ref-0-id-405
 | 
prop lemma from negated double imply
 | 
| 
ref-0-id-406
 | 
prop lemma from negated and
 | 
| 
ref-0-id-407
 | 
prop lemma from negated or
 | 
| 
ref-0-id-408
 | 
prop lemma to negated or
 | 
| 
ref-0-id-409
 | 
prop lemma from negations
 | 
| 
ref-0-id-410
 | 
prop lemma from three disjuncts
 | 
| 
ref-0-id-411
 | 
prop lemma from two times two disjuncts
 | 
| 
ref-0-id-412
 | 
prop lemma negate first disjunct
 | 
| 
ref-0-id-413
 | 
prop lemma negate second disjunct
 | 
| 
ref-0-id-414
 | 
prop lemma expand disjuncts
 | 
| 
ref-0-id-415
 | 
lemma set equality nec condition(1)
 | 
| 
ref-0-id-416
 | 
lemma set equality nec condition(2)
 | 
| 
ref-0-id-417
 | 
lemma lessLeq(R)
 | 
| 
ref-0-id-418
 | 
lemma memberOfSeries
 | 
| 
ref-0-id-419
 | 
lemma memberOfSeries(Type)
 | 
| 
ref-0-id-420
 | 
{MissingArg} ^ {MissingArg}
 | 
| 
ref-0-id-421
 | 
R( {MissingArg} )
 | 
| 
ref-0-id-422
 | 
--R( {MissingArg} )
 | 
| 
ref-0-id-423
 | 
1/ {MissingArg}
 | 
| 
ref-0-id-424
 | 
eq-system of {MissingArg} modulo {MissingArg}
 | 
| 
ref-0-id-425
 | 
intersection {MissingArg} comma {MissingArg} end intersection
 | 
| 
ref-0-id-426
 | 
[ {MissingArg} ; {MissingArg} ]
 | 
| 
ref-0-id-427
 | 
union {MissingArg} end union
 | 
| 
ref-0-id-428
 | 
binary-union {MissingArg} comma {MissingArg} end union
 | 
| 
ref-0-id-429
 | 
power {MissingArg} end power
 | 
| 
ref-0-id-430
 | 
zermelo singleton {MissingArg} end singleton
 | 
| 
ref-0-id-431
 | 
stateExpand( {MissingArg} , {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-432
 | 
extractSeries( {MissingArg} )
 | 
| 
ref-0-id-433
 | 
setOfSeries( {MissingArg} )
 | 
| 
ref-0-id-434
 | 
--Macro( {MissingArg} )
 | 
| 
ref-0-id-435
 | 
expandList( {MissingArg} , {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-436
 | 
**Macro( {MissingArg} )
 | 
| 
ref-0-id-437
 | 
++Macro( {MissingArg} )
 | 
| 
ref-0-id-438
 | 
<
 | 
| 
ref-0-id-439
 | 
||Macro( {MissingArg} )
 | 
| 
ref-0-id-440
 | 
01//Macro( {MissingArg} )
 | 
| 
ref-0-id-441
 | 
upperBound( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-442
 | 
leastUpperBound( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-443
 | 
base(1/2)Sum( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-444
 | 
UStelescope( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-445
 | 
( {MissingArg} )
 | 
| 
ref-0-id-446
 | 
|f {MissingArg} |
 | 
| 
ref-0-id-447
 | 
|r {MissingArg} |
 | 
| 
ref-0-id-448
 | 
limit( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-449
 | 
U( {MissingArg} )
 | 
| 
ref-0-id-450
 | 
isOrderedPair( {MissingArg} , {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-451
 | 
isRelation( {MissingArg} , {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-452
 | 
isFunction( {MissingArg} , {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-453
 | 
isSeries( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-454
 | 
isNatural( {MissingArg} )
 | 
| 
ref-0-id-455
 | 
(o {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-456
 | 
typeNat( {MissingArg} )
 | 
| 
ref-0-id-457
 | 
typeNat0( {MissingArg} )
 | 
| 
ref-0-id-458
 | 
typeRational( {MissingArg} )
 | 
| 
ref-0-id-459
 | 
typeRational0( {MissingArg} )
 | 
| 
ref-0-id-460
 | 
typeSeries( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-461
 | 
typeSeries0( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-462
 | 
zermelo pair {MissingArg} comma {MissingArg} end pair
 | 
| 
ref-0-id-463
 | 
zermelo ordered pair {MissingArg} comma {MissingArg} end pair
 | 
| 
ref-0-id-464
 | 
- {MissingArg}
 | 
| 
ref-0-id-465
 | 
-f {MissingArg}
 | 
| 
ref-0-id-466
 | 
-- {MissingArg}
 | 
| 
ref-0-id-467
 | 
1f/ {MissingArg}
 | 
| 
ref-0-id-468
 | 
01// {MissingArg}
 | 
| 
ref-0-id-469
 | 
{MissingArg} is related to {MissingArg} under {MissingArg}
 | 
| 
ref-0-id-470
 | 
{MissingArg} is reflexive relation in {MissingArg}
 | 
| 
ref-0-id-471
 | 
{MissingArg} is symmetric relation in {MissingArg}
 | 
| 
ref-0-id-472
 | 
{MissingArg} is transitive relation in {MissingArg}
 | 
| 
ref-0-id-473
 | 
{MissingArg} is equivalence relation in {MissingArg}
 | 
| 
ref-0-id-474
 | 
equivalence class of {MissingArg} in {MissingArg} modulo {MissingArg}
 | 
| 
ref-0-id-475
 | 
{MissingArg} is partition of {MissingArg}
 | 
| 
ref-0-id-476
 | 
{MissingArg} * {MissingArg}
 | 
| 
ref-0-id-477
 | 
{MissingArg} *f {MissingArg}
 | 
| 
ref-0-id-478
 | 
{MissingArg} ** {MissingArg}
 | 
| 
ref-0-id-479
 | 
{MissingArg} + {MissingArg}
 | 
| 
ref-0-id-480
 | 
{MissingArg} - {MissingArg}
 | 
| 
ref-0-id-481
 | 
{MissingArg} +f {MissingArg}
 | 
| 
ref-0-id-482
 | 
{MissingArg} -f {MissingArg}
 | 
| 
ref-0-id-483
 | 
{MissingArg} ++ {MissingArg}
 | 
| 
ref-0-id-484
 | 
R( {MissingArg} ) -- R( {MissingArg} )
 | 
| 
ref-0-id-485
 | 
{MissingArg} in0 {MissingArg}
 | 
| 
ref-0-id-486
 | 
| {MissingArg} |
 | 
| 
ref-0-id-487
 | 
if( {MissingArg} , {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-488
 | 
max( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-489
 | 
maxR( {MissingArg} , {MissingArg} )
 | 
| 
ref-0-id-490
 | 
{MissingArg} = {MissingArg}
 | 
| 
ref-0-id-491
 | 
{MissingArg} != {MissingArg}
 | 
| 
ref-0-id-492
 | 
{MissingArg} <= {MissingArg}
 | 
| 
ref-0-id-493
 | 
{MissingArg} < {MissingArg}
 | 
| 
ref-0-id-494
 | 
{MissingArg} 
 | 
| 
ref-0-id-495
 | 
{MissingArg} <=f {MissingArg}
 | 
| 
ref-0-id-496
 | 
{MissingArg} sameF {MissingArg}
 | 
| 
ref-0-id-497
 | 
{MissingArg} == {MissingArg}
 | 
| 
ref-0-id-498
 | 
{MissingArg} !!== {MissingArg}
 | 
| 
ref-0-id-499
 | 
{MissingArg} << {MissingArg}
 | 
| 
ref-0-id-500
 | 
{MissingArg} <<== {MissingArg}
 | 
| 
ref-0-id-501
 | 
{MissingArg} zermelo is {MissingArg}
 | 
| 
ref-0-id-502
 | 
{MissingArg} is subset of {MissingArg}
 | 
| 
ref-0-id-503
 | 
not0 {MissingArg}
 | 
| 
ref-0-id-504
 | 
{MissingArg} zermelo ~in {MissingArg}
 | 
| 
ref-0-id-505
 | 
{MissingArg} zermelo ~is {MissingArg}
 | 
| 
ref-0-id-506
 | 
{MissingArg} and0 {MissingArg}
 | 
| 
ref-0-id-507
 | 
{MissingArg} or0 {MissingArg}
 | 
| 
ref-0-id-508
 | 
exist0 {MissingArg} indeed {MissingArg}
 | 
| 
ref-0-id-509
 | 
{MissingArg} iff {MissingArg}
 | 
| 
ref-0-id-510
 | 
the set of ph in {MissingArg} such that {MissingArg} end set
 |