| 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,