0 | 0 | am |
1 | 0 | cdots |
2 | 0 | object-var |
3 | 0 | ex-var |
4 | 0 | ph-var |
5 | 0 | vaerdi |
6 | 0 | variabel |
7 | 1 | op {MissingArg} end op |
8 | 2 | op2 {MissingArg} comma {MissingArg} end op2 |
9 | 2 | define-equal {MissingArg} comma {MissingArg} end equal |
10 | 1 | contains-empty {MissingArg} end empty |
11 | 2 | 1deduction {MissingArg} conclude {MissingArg} end 1deduction |
12 | 2 | 1deduction zero {MissingArg} conclude {MissingArg} end 1deduction |
13 | 3 | 1deduction side {MissingArg} conclude {MissingArg} condition {MissingArg} end 1deduction |
14 | 3 | 1deduction one {MissingArg} conclude {MissingArg} condition {MissingArg} end 1deduction |
15 | 3 | 1deduction two {MissingArg} conclude {MissingArg} condition {MissingArg} end 1deduction |
16 | 4 | 1deduction three {MissingArg} conclude {MissingArg} condition {MissingArg} bound {MissingArg} end 1deduction |
17 | 4 | 1deduction four {MissingArg} conclude {MissingArg} condition {MissingArg} bound {MissingArg} end 1deduction |
18 | 4 | 1deduction four star {MissingArg} conclude {MissingArg} condition {MissingArg} bound {MissingArg} end 1deduction |
19 | 3 | 1deduction five {MissingArg} condition {MissingArg} bound {MissingArg} end 1deduction |
20 | 4 | 1deduction six {MissingArg} conclude {MissingArg} exception {MissingArg} bound {MissingArg} end 1deduction |
21 | 4 | 1deduction six star {MissingArg} conclude {MissingArg} exception {MissingArg} bound {MissingArg} end 1deduction |
22 | 1 | 1deduction seven {MissingArg} end 1deduction |
23 | 2 | 1deduction eight {MissingArg} bound {MissingArg} end 1deduction |
24 | 2 | 1deduction eight star {MissingArg} bound {MissingArg} end 1deduction |
25 | 0 | ex1 |
26 | 0 | ex2 |
27 | 0 | ex3 |
28 | 0 | ex10 |
29 | 0 | ex20 |
30 | 1 | existential var {MissingArg} end var |
31 | 1 | {MissingArg} is existential var |
32 | 4 | exist-sub {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub |
33 | 4 | exist-sub0 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub |
34 | 4 | exist-sub1 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub |
35 | 4 | exist-sub* {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub |
36 | 0 | placeholder-var1 |
37 | 0 | placeholder-var2 |
38 | 0 | placeholder-var3 |
39 | 1 | placeholder-var {MissingArg} end var |
40 | 1 | {MissingArg} is placeholder-var |
41 | 4 | ph-sub {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub |
42 | 4 | ph-sub0 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub |
43 | 4 | ph-sub1 {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub |
44 | 4 | ph-sub* {MissingArg} is {MissingArg} where {MissingArg} is {MissingArg} end sub |
45 | 0 | var big set |
46 | 0 | object big set |
47 | 0 | meta big set |
48 | 0 | zermelo empty set |
49 | 0 | system Q |
50 | 0 | 1rule mp |
51 | 0 | 1rule gen |
52 | 0 | 1rule repetition |
53 | 0 | 1rule ad absurdum |
54 | 0 | 1rule deduction |
55 | 0 | 1rule exist intro |
56 | 0 | axiom extensionality |
57 | 0 | axiom empty set |
58 | 0 | axiom pair definition |
59 | 0 | axiom union definition |
60 | 0 | axiom power definition |
61 | 0 | axiom separation definition |
62 | 0 | prop lemma add double neg |
63 | 0 | prop lemma remove double neg |
64 | 0 | prop lemma and commutativity |
65 | 0 | prop lemma auto imply |
66 | 0 | prop lemma contrapositive |
67 | 0 | prop lemma first conjunct |
68 | 0 | prop lemma second conjunct |
69 | 0 | prop lemma from contradiction |
70 | 0 | prop lemma from disjuncts |
71 | 0 | prop lemma iff commutativity |
72 | 0 | prop lemma iff first |
73 | 0 | prop lemma iff second |
74 | 0 | prop lemma imply transitivity |
75 | 0 | prop lemma join conjuncts |
76 | 0 | prop lemma mp2 |
77 | 0 | prop lemma mp3 |
78 | 0 | prop lemma mp4 |
79 | 0 | prop lemma mp5 |
80 | 0 | prop lemma mt |
81 | 0 | prop lemma negative mt |
82 | 0 | prop lemma technicality |
83 | 0 | prop lemma weakening |
84 | 0 | prop lemma weaken or first |
85 | 0 | prop lemma weaken or second |
86 | 0 | lemma formula2pair |
87 | 0 | lemma pair2formula |
88 | 0 | lemma formula2union |
89 | 0 | lemma union2formula |
90 | 0 | lemma formula2separation |
91 | 0 | lemma separation2formula |
92 | 0 | lemma subset in power set |
93 | 0 | lemma power set is subset0 |
94 | 0 | lemma power set is subset |
95 | 0 | lemma power set is subset0-switch |
96 | 0 | lemma power set is subset-switch |
97 | 0 | lemma set equality suff condition |
98 | 0 | lemma set equality suff condition(t)0 |
99 | 0 | lemma set equality suff condition(t) |
100 | 0 | lemma set equality skip quantifier |
101 | 0 | lemma set equality nec condition |
102 | 0 | lemma reflexivity0 |
103 | 0 | lemma reflexivity |
104 | 0 | lemma symmetry0 |
105 | 0 | lemma symmetry |
106 | 0 | lemma transitivity0 |
107 | 0 | lemma transitivity |
108 | 0 | lemma er is reflexive |
109 | 0 | lemma er is symmetric |
110 | 0 | lemma er is transitive |
111 | 0 | lemma empty set is subset |
112 | 0 | lemma member not empty0 |
113 | 0 | lemma member not empty |
114 | 0 | lemma unique empty set0 |
115 | 0 | lemma unique empty set |
116 | 0 | lemma ==Reflexivity |
117 | 0 | lemma ==Symmetry |
118 | 0 | lemma ==Transitivity0 |
119 | 0 | lemma ==Transitivity |
120 | 0 | lemma transfer ~is0 |
121 | 0 | lemma transfer ~is |
122 | 0 | lemma pair subset0 |
123 | 0 | lemma pair subset1 |
124 | 0 | lemma pair subset |
125 | 0 | lemma same pair |
126 | 0 | lemma same singleton |
127 | 0 | lemma union subset |
128 | 0 | lemma same union |
129 | 0 | lemma separation subset |
130 | 0 | lemma same separation |
131 | 0 | lemma same binary union |
132 | 0 | lemma intersection subset |
133 | 0 | lemma same intersection |
134 | 0 | lemma auto member |
135 | 0 | lemma eq-system not empty0 |
136 | 0 | lemma eq-system not empty |
137 | 0 | lemma eq subset0 |
138 | 0 | lemma eq subset |
139 | 0 | lemma equivalence nec condition0 |
140 | 0 | lemma equivalence nec condition |
141 | 0 | lemma none-equivalence nec condition0 |
142 | 0 | lemma none-equivalence nec condition1 |
143 | 0 | lemma none-equivalence nec condition |
144 | 0 | lemma equivalence class is subset |
145 | 0 | lemma equivalence classes are disjoint |
146 | 0 | lemma all disjoint |
147 | 0 | lemma all disjoint-imply |
148 | 0 | lemma bs subset union(bs/r) |
149 | 0 | lemma union(bs/r) subset bs |
150 | 0 | lemma union(bs/r) is bs |
151 | 0 | theorem eq-system is partition |
152 | 0 | var ep |
153 | 0 | var fx |
154 | 0 | var fy |
155 | 0 | var fz |
156 | 0 | var fu |
157 | 0 | var fv |
158 | 0 | var rx |
159 | 0 | var ry |
160 | 0 | var rz |
161 | 0 | var ru |
162 | 0 | meta ep |
163 | 0 | meta fx |
164 | 0 | meta fy |
165 | 0 | meta fz |
166 | 0 | meta fu |
167 | 0 | meta fv |
168 | 0 | meta rx |
169 | 0 | meta ry |
170 | 0 | meta rz |
171 | 0 | meta ru |
172 | 0 | 0 |
173 | 0 | 1 |
174 | 0 | (-1) |
175 | 0 | 2 |
176 | 0 | 1/2 |
177 | 0 | 0f |
178 | 0 | 1f |
179 | 0 | 00 |
180 | 0 | 01 |
181 | 0 | axiom leqReflexivity |
182 | 0 | axiom leqAntisymmetry |
183 | 0 | axiom leqTransitivity |
184 | 0 | axiom leqTotality |
185 | 0 | axiom leqAddition |
186 | 0 | axiom leqMultiplication |
187 | 0 | axiom plusAssociativity |
188 | 0 | axiom plusCommutativity |
189 | 0 | axiom negative |
190 | 0 | axiom plus0 |
191 | 0 | axiom timesAssociativity |
192 | 0 | axiom timesCommutativity |
193 | 0 | axiom reciprocal |
194 | 0 | axiom times1 |
195 | 0 | axiom distribution |
196 | 0 | axiom 0not1 |
197 | 0 | axiom equality |
198 | 0 | axiom eqLeq |
199 | 0 | axiom eqAddition |
200 | 0 | axiom eqMultiplication |
201 | 0 | lemma set equality nec condition(1) |
202 | 0 | lemma set equality nec condition(2) |
203 | 0 | 1rule ifThenElse true |
204 | 0 | 1rule ifThenElse false |
205 | 0 | 1rule from=f |
206 | 0 | 1rule to=f |
207 | 0 |
1rule from |
208 | 0 |
1rule to |
209 | 0 | axiom plusF |
210 | 0 | axiom timesF |
211 | 0 | axiom minusF |
212 | 0 | axiom 0f |
213 | 0 | axiom 1f |
214 | 0 | 1rule fromSameF |
215 | 0 | 1rule toSameF |
216 | 0 | 1rule to==XX |
217 | 0 | 1rule from== |
218 | 0 | 1rule to== |
219 | 0 |
1rule from< |
220 | 0 |
1rule from< |
221 | 0 |
1rule from< |
222 | 0 |
1rule to< |
223 | 0 | 1rule from<< |
224 | 0 | 1rule to<< |
225 | 0 | 1rule fromInR |
226 | 0 | axiom plusR |
227 | 0 | axiom timesR |
228 | 0 | lemma leqAntisymmetry |
229 | 0 | lemma leqTransitivity |
230 | 0 | lemma leqAddition |
231 | 0 | lemma leqMultiplication |
232 | 0 | lemma reciprocal |
233 | 0 | lemma equality |
234 | 0 | lemma eqLeq |
235 | 0 | lemma eqAddition |
236 | 0 | lemma eqMultiplication |
237 | 0 | prop lemma to negated imply |
238 | 0 | prop lemma tertium non datur |
239 | 0 | prop lemma imply negation |
240 | 0 | prop lemma from negations |
241 | 0 | prop lemma from three disjuncts |
242 | 0 | prop lemma from two times two disjuncts |
243 | 0 | prop lemma negate first disjunct |
244 | 0 | prop lemma negate second disjunct |
245 | 0 | prop lemma expand disjuncts |
246 | 0 | lemma eqReflexivity |
247 | 0 | lemma eqSymmetry |
248 | 0 | lemma eqTransitivity |
249 | 0 | lemma eqTransitivity4 |
250 | 0 | lemma eqTransitivity5 |
251 | 0 | lemma eqTransitivity6 |
252 | 0 | lemma plus0Left |
253 | 0 | lemma times1Left |
254 | 0 | lemma eqAdditionLeft |
255 | 0 | lemma eqMultiplicationLeft |
256 | 0 | lemma distributionOut |
257 | 0 | lemma three2twoTerms |
258 | 0 | lemma three2threeTerms |
259 | 0 | lemma three2twoFactors |
260 | 0 | lemma addEquations |
261 | 0 | lemma subtractEquations |
262 | 0 | lemma subtractEquationsLeft |
263 | 0 | lemma eqNegated |
264 | 0 | lemma positiveToRight(Eq) |
265 | 0 | lemma positiveToLeft(Eq)(1 term) |
266 | 0 | lemma negativeToLeft(Eq) |
267 | 0 | lemma lessNeq |
268 | 0 | lemma neqSymmetry |
269 | 0 | lemma neqNegated |
270 | 0 | lemma subNeqRight |
271 | 0 | lemma subNeqLeft |
272 | 0 | lemma neqAddition |
273 | 0 | lemma neqMultiplication |
274 | 0 | lemma uniqueNegative |
275 | 0 | lemma doubleMinus |
276 | 0 | lemma leqLessEq |
277 | 0 | lemma lessLeq |
278 | 0 | lemma from leqGeq |
279 | 0 | lemma subLeqRight |
280 | 0 | lemma subLeqLeft |
281 | 0 | lemma leqPlus1 |
282 | 0 | lemma positiveToRight(Leq) |
283 | 0 | lemma positiveToRight(Leq)(1 term) |
284 | 0 | lemma negativeToLeft(Leq) |
285 | 0 | lemma leqAdditionLeft |
286 | 0 | lemma leqSubtraction |
287 | 0 | lemma leqSubtractionLeft |
288 | 0 | lemma thirdGeq |
289 | 0 | lemma leqNegated |
290 | 0 | lemma addEquations(Leq) |
291 | 0 | lemma thirdGeqSeries |
292 | 0 | lemma leqNeqLess |
293 | 0 | lemma fromLess |
294 | 0 | lemma toLess |
295 | 0 | lemma fromNotLess |
296 | 0 | lemma toNotLess |
297 | 0 | lemma negativeLessPositive |
298 | 0 | lemma leqLessTransitivity |
299 | 0 | lemma lessLeqTransitivity |
300 | 0 | lemma lessTransitivity |
301 | 0 | lemma lessTotality |
302 | 0 | lemma subLessRight |
303 | 0 | lemma subLessLeft |
304 | 0 | lemma lessAddition |
305 | 0 | lemma lessAdditionLeft |
306 | 0 | lemma lessMultiplication |
307 | 0 | lemma lessMultiplicationLeft |
308 | 0 | lemma lessDivision |
309 | 0 | lemma addEquations(Less) |
310 | 0 | lemma lessNegated |
311 | 0 | lemma positiveNegated |
312 | 0 | lemma nonpositiveNegated |
313 | 0 | lemma negativeNegated |
314 | 0 | lemma nonnegativeNegated |
315 | 0 | lemma positiveHalved |
316 | 0 | lemma nonnegativeNumerical |
317 | 0 | lemma negativeNumerical |
318 | 0 | lemma positiveNumerical |
319 | 0 | lemma nonpositiveNumerical |
320 | 0 | lemma |0|=0 |
321 | 0 | lemma 0<=|x| |
322 | 0 | lemma sameNumerical |
323 | 0 | lemma signNumerical(+) |
324 | 0 | lemma signNumerical |
325 | 0 | lemma numericalDifference |
326 | 0 | lemma splitNumericalSumHelper |
327 | 0 | lemma splitNumericalSum(++) |
328 | 0 | lemma splitNumericalSum(--) |
329 | 0 | lemma splitNumericalSum(+-, smallNegative) |
330 | 0 | lemma splitNumericalSum(+-, bigNegative) |
331 | 0 | lemma splitNumericalSum(+-) |
332 | 0 | lemma splitNumericalSum(-+) |
333 | 0 | lemma splitNumericalSum |
334 | 0 | lemma insertMiddleTerm(Numerical) |
335 | 0 | lemma x+y=zBackwards |
336 | 0 | lemma x*y=zBackwards |
337 | 0 | lemma x=x+(y-y) |
338 | 0 | lemma x=x+y-y |
339 | 0 | lemma x=x*y*(1/y) |
340 | 0 | lemma insertMiddleTerm(Sum) |
341 | 0 | lemma insertMiddleTerm(Difference) |
342 | 0 | lemma x*0+x=x |
343 | 0 | lemma x*0=0 |
344 | 0 | lemma (-1)*(-1)+(-1)*1=0 |
345 | 0 | lemma (-1)*(-1)=1 |
346 | 0 | lemma 0<1Helper |
347 | 0 | lemma 0<1 |
348 | 0 | lemma 0<2 |
349 | 0 | lemma 0<1/2 |
350 | 0 | lemma x+x=2*x |
351 | 0 | lemma (1/2)x+(1/2)x=x |
352 | 0 | lemma -x-y=-(x+y) |
353 | 0 | lemma minusNegated |
354 | 0 | lemma times(-1) |
355 | 0 | lemma times(-1)Left |
356 | 0 | lemma -0=0 |
357 | 0 | lemma sameFsymmetry |
358 | 0 | lemma sameFtransitivity |
359 | 0 | lemma =f to sameF |
360 | 0 | lemma plusF(Sym) |
361 | 0 | lemma timesF(Sym) |
362 | 0 | lemma f2R(Plus) |
363 | 0 | lemma f2R(Times) |
364 | 0 | lemma plusR(Sym) |
365 | 0 | lemma timesR(Sym) |
366 | 0 | lemma lessLeq(R) |
367 | 0 | lemma eqLeq(R) |
368 | 0 | lemma subLessRight(R) |
369 | 0 | lemma subLessLeft(R) |
370 | 0 |
lemma < |
371 | 0 |
lemma < |
372 | 0 | lemma <<==Reflexivity |
373 | 0 | lemma <<==AntisymmetryHelper(Q) |
374 | 0 | lemma <<==Antisymmetry |
375 | 0 | lemma <<==Transitivity |
376 | 0 | lemma plus0f |
377 | 0 | lemma plus00 |
378 | 0 | lemma ==Addition |
379 | 0 | lemma ==AdditionLeft |
380 | 0 |
lemma < |
381 | 0 | lemma <<==Addition |
382 | 0 | lemma plusAssociativity(F) |
383 | 0 | lemma plusAssociativity(R) |
384 | 0 | lemma negative(R) |
385 | 0 | lemma plusCommutativity(F) |
386 | 0 | lemma plusCommutativity(R) |
387 | 0 | lemma timesAssociativity(F) |
388 | 0 | lemma timesAssociativity(R) |
389 | 0 | lemma times1f |
390 | 0 | lemma times01 |
391 | 0 | lemma timesCommutativity(F) |
392 | 0 | lemma timesCommutativity(R) |
393 | 0 | lemma distribution(F) |
394 | 0 | lemma distribution(R) |
395 | 1 | R( {MissingArg} ) |
396 | 1 | --R( {MissingArg} ) |
397 | 1 | 1/ {MissingArg} |
398 | 2 | eq-system of {MissingArg} modulo {MissingArg} |
399 | 2 | intersection {MissingArg} comma {MissingArg} end intersection |
400 | 2 | [ {MissingArg} ; {MissingArg} ] |
401 | 1 | union {MissingArg} end union |
402 | 2 | binary-union {MissingArg} comma {MissingArg} end union |
403 | 1 | power {MissingArg} end power |
404 | 1 | zermelo singleton {MissingArg} end singleton |
405 | 2 | zermelo pair {MissingArg} comma {MissingArg} end pair |
406 | 2 | zermelo ordered pair {MissingArg} comma {MissingArg} end pair |
407 | 1 | - {MissingArg} |
408 | 1 | -f {MissingArg} |
409 | 2 | {MissingArg} in0 {MissingArg} |
410 | 3 | {MissingArg} is related to {MissingArg} under {MissingArg} |
411 | 2 | {MissingArg} is reflexive relation in {MissingArg} |
412 | 2 | {MissingArg} is symmetric relation in {MissingArg} |
413 | 2 | {MissingArg} is transitive relation in {MissingArg} |
414 | 2 | {MissingArg} is equivalence relation in {MissingArg} |
415 | 3 | equivalence class of {MissingArg} in {MissingArg} modulo {MissingArg} |
416 | 2 | {MissingArg} is partition of {MissingArg} |
417 | 2 | {MissingArg} * {MissingArg} |
418 | 2 | {MissingArg} *f {MissingArg} |
419 | 2 | {MissingArg} ** {MissingArg} |
420 | 2 | {MissingArg} + {MissingArg} |
421 | 2 | {MissingArg} - {MissingArg} |
422 | 2 | {MissingArg} +f {MissingArg} |
423 | 2 | {MissingArg} -f {MissingArg} |
424 | 2 | {MissingArg} ++ {MissingArg} |
425 | 2 | R( {MissingArg} ) -- R( {MissingArg} ) |
426 | 1 | | {MissingArg} | |
427 | 3 | if( {MissingArg} , {MissingArg} , {MissingArg} ) |
428 | 2 | {MissingArg} = {MissingArg} |
429 | 2 | {MissingArg} != {MissingArg} |
430 | 2 | {MissingArg} <= {MissingArg} |
431 | 2 | {MissingArg} < {MissingArg} |
432 | 2 | {MissingArg} =f {MissingArg} |
433 | 2 |
{MissingArg} |
434 | 2 | {MissingArg} sameF {MissingArg} |
435 | 2 | {MissingArg} == {MissingArg} |
436 | 2 | {MissingArg} << {MissingArg} |
437 | 2 | {MissingArg} <<== {MissingArg} |
438 | 2 | {MissingArg} zermelo is {MissingArg} |
439 | 2 | {MissingArg} is subset of {MissingArg} |
440 | 1 | not0 {MissingArg} |
441 | 2 | {MissingArg} zermelo ~in {MissingArg} |
442 | 2 | {MissingArg} zermelo ~is {MissingArg} |
443 | 2 | {MissingArg} and0 {MissingArg} |
444 | 2 | {MissingArg} or0 {MissingArg} |
445 | 2 | {MissingArg} iff {MissingArg} |
446 | 2 | the set of ph in {MissingArg} such that {MissingArg} end set |
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,