| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , , ⊢ ![](../d8fa552a7b5a429afc0c4dd89d780c552fda6a0d0/expr.png) |
| : , : , : ![](../a02a79c479cf865ecf3d0cfc4048064cecbe03f20/expr.png) |
1 | reference | 8 | ⊢ ![](../../../../../logic/equality/__pv_it/axioms/b5b3cf1e74e7e4fc2d5f197f08b661e6992950090/expr.png) |
2 | instantiation | 8, 4, 5 | , , ⊢ ![](../0ba4d2fe70c24a1afccf3a0851caf1b52f8a27670/expr.png) |
| : , : , : ![](../b504dd215d7404da8eb34bf43e2b73bcd1c270940/expr.png) |
3 | instantiation | 17, 6, 50, 20, 7, 13, 23, 24, 25, 26, 29, 27, 28 | , , ⊢ ![](../8c4f71de13ca726458c3f9f8c6b0c749a25587a60/expr.png) |
| : , : , : , : , : , : , : ![](../../axioms/1a4193f1deeaf7a4a6b6289328d46189ae6a257f0/expr.png) |
4 | instantiation | 8, 9, 10 | , , ⊢ ![](../3b5c9f0cac1dd1c2f0e258ebfff35fdd77105d5c0/expr.png) |
| : , : , : ![](../8bfa2f4fc99ad7cb999f00b8116d8e79e4544bb30/expr.png) |
5 | instantiation | 17, 11, 50, 49, 12, 13, 24, 25, 26, 29, 27, 28 | , , ⊢ ![](../d86366119ccc770f47418eab3c9c622f4098ee010/expr.png) |
| : , : , : , : , : , : , : ![](../../../subtraction/__pv_it/theorems/25c776cc10fb7df90a1cddbf8213d6561f6b7bd20/expr.png) |
6 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/29dd1507dc5b38745f0e5bd500c91e1943afb7450/expr.png) |
| proveit.numbers.numerals.decimals.nat7 |
7 | instantiation | 14 | ⊢ ![](../cc3467b9fcb38813e76da97ea585c96199430a3a0/expr.png) |
| : , : , : , : , : , : , : ![](../../../../../__pv_it/common/ceef4280a2f1cc604b455b54e735507244cc62cd0/expr.png) |
8 | axiom | | ⊢ ![](../../../../../logic/equality/__pv_it/axioms/b5b3cf1e74e7e4fc2d5f197f08b661e6992950090/expr.png) |
| proveit.logic.equality.equals_transitivity |
9 | instantiation | 17, 49, 18, 15, 16, 24, 25, 26, 27, 28, 29 | , , ⊢ ![](../48960cb9cad88290434756e92531f6f5ea2531cf0/expr.png) |
| : , : , : , : , : , : , : ![](../bdaa48644e83a918c8123f2337b35e8b465a52180/expr.png) |
10 | instantiation | 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 | , , ⊢ ![](../4aedcb0f09947485a68530116399d78473f54c750/expr.png) |
| : , : , : , : , : , : , : ![](../../axioms/1a4193f1deeaf7a4a6b6289328d46189ae6a257f0/expr.png) |
11 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/e8c4ac0b8d6c7ee7c2032b056029bbdf8777001e0/expr.png) |
| proveit.numbers.numerals.decimals.nat6 |
12 | instantiation | 30 | ⊢ ![](../bbc1fb25da5e98aedb1a0cf2f9f98bc5d1f6b3970/expr.png) |
| : , : , : , : , : , : ![](../../../../../__pv_it/common/ceef4280a2f1cc604b455b54e735507244cc62cd0/expr.png) |
13 | instantiation | 31 | ⊢ ![](../1dc7d7d6c56aef45a5b7477f943e7dbb2cbb39f40/expr.png) |
| : , : ![](../../../../../__pv_it/common/195236b98c6c564a75b5dbada74b173bc52d5c3e0/expr.png) |
14 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/06278e8dc731cd89b11008159f618afd521f83180/expr.png) |
| proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
15 | instantiation | 32 | ⊢ ![](../d52fce3b1e14ffa5011941c131daecad59db9af60/expr.png) |
| : , : , : , : ![](../../../../../__pv_it/common/195236b98c6c564a75b5dbada74b173bc52d5c3e0/expr.png) |
16 | instantiation | 32 | ⊢ ![](../012b00bc4ea55fab7863077e3dbde05f1e29555c0/expr.png) |
| : , : , : , : ![](../../../../numerals/__pv_it/common/1943b60945420e340d305780feff5c1aff2740ff0/expr.png) |
17 | theorem | | ⊢ ![](../../theorems/ce884f4ddc455e8aa5ab1ea3923b843a3059b1340/expr.png) |
| proveit.numbers.addition.leftward_commutation |
18 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/5cf9097f623478f61147fb5f5c8bbd61d83cfe3a0/expr.png) |
| proveit.numbers.numerals.decimals.nat4 |
19 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/508b27c60c15225368b6f1207f71166a39da216d0/expr.png) |
| proveit.numbers.numerals.decimals.nat5 |
20 | axiom | | ⊢ ![](../../../../number_sets/natural_numbers/__pv_it/axioms/6bc27fa16ea1c04bf3d4c776d5c721085150bfa20/expr.png) |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
21 | instantiation | 32 | ⊢ ![](../e914073fc52c87ade703b6633066a58be92d44630/expr.png) |
| : , : , : , : ![](../../../../numerals/__pv_it/common/af4aab8a07465db063742696e006d04670f30cf10/expr.png) |
22 | instantiation | 33 | ⊢ ![](../ce123ece1e3d0fd3f5d43c4ec89fc02f0e5a82160/expr.png) |
| : , : , : , : , : ![](../../../../../__pv_it/common/ceef4280a2f1cc604b455b54e735507244cc62cd0/expr.png) |
23 | theorem | | ⊢ ![](../../../../../core_expr_types/tuples/__pv_it/theorems/e4227b9c4c4eee791197a50fb372df0303979ecf0/expr.png) |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
24 | instantiation | 51, 39, 34 | ⊢ ![](../../theorems/e9f87a0977d5044ea8daf1040d2f219396bb3d5b0/expr.png) |
| : , : , : ![](../../../../../__pv_it/common/c06c606ec12678c58933ac85412ecadc2ae28be60/expr.png) |
25 | instantiation | 51, 39, 35 | ⊢ ![](../90bf3c2d089cebf5c6c26ab03764c801f4f029cd0/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/682157d4892d216d9e5626ed533aff9b56b9506e0/expr.png) |
26 | instantiation | 51, 39, 36 | ⊢ ![](../2c4bd2670ea1c897df5369ee136bb00ac765f0ee0/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/af4aab8a07465db063742696e006d04670f30cf10/expr.png) |
27 | instantiation | 51, 39, 37 | ⊢ ![](../../theorems/b66b5547fa9b0b910f79351152926c658c2718190/expr.png) |
| : , : , : ![](../../../../../__pv_it/common/ceef4280a2f1cc604b455b54e735507244cc62cd0/expr.png) |
28 | instantiation | 51, 39, 38 | ⊢ ![](../../theorems/a259ec76dfb0a5be60b7c83d797520fa82c1dba60/expr.png) |
| : , : , : ![](../../../../../__pv_it/common/195236b98c6c564a75b5dbada74b173bc52d5c3e0/expr.png) |
29 | instantiation | 51, 39, 40 | ⊢ ![](../b7c0ab46a80fa49f5f87317ac1bbf9cb271ca9e60/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/1943b60945420e340d305780feff5c1aff2740ff0/expr.png) |
30 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/995b6f3b19b4482310051f0f61a84b78d01252bc0/expr.png) |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
31 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/10b037baccf1e1ebd13cf393d16f9c41951216fd0/expr.png) |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
32 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/1e5f5f56d23c5d2fa392d75922cfebe52e53ebbd0/expr.png) |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
33 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/339998d4e03211b77c8a5fbbc9b3d3593022789a0/expr.png) |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
34 | assumption | | ⊢ ![](../../../../ordering/__pv_it/theorems/4aa8d696b1f407d6126de9f51a052e8d90e0848c0/expr.png) |
35 | instantiation | 51, 43, 41 | ⊢ ![](../815f4888a8cac98a73326f5b7485c31114afb1fc0/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/682157d4892d216d9e5626ed533aff9b56b9506e0/expr.png) |
36 | instantiation | 51, 43, 42 | ⊢ ![](../371d48b3894e95e20b50c9d70ca5e18a2adb54990/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/af4aab8a07465db063742696e006d04670f30cf10/expr.png) |
37 | assumption | | ⊢ ![](../d550e8309ef79ca46e4c9fb5617a392ea678789b0/expr.png) |
38 | assumption | | ⊢ ![](../../../../ordering/__pv_it/theorems/6e5cad5b2984ed0d75bd47bd0c542ec447a4f3570/expr.png) |
39 | theorem | | ⊢ ![](../../../../number_sets/complex_numbers/__pv_it/theorems/38989098df56675752c00127b89e7c6d9bdcbcf90/expr.png) |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
40 | instantiation | 51, 43, 44 | ⊢ ![](../461319c14ad605ae443f7641bdd5329eb9aaaa9e0/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/1943b60945420e340d305780feff5c1aff2740ff0/expr.png) |
41 | instantiation | 51, 47, 45 | ⊢ ![](../40990e006b64102ede007d95d331ea850c17ba800/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/682157d4892d216d9e5626ed533aff9b56b9506e0/expr.png) |
42 | instantiation | 51, 47, 46 | ⊢ ![](../9fcd7e1f9f79a43396482feffbef8cf6ef083bbd0/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/af4aab8a07465db063742696e006d04670f30cf10/expr.png) |
43 | theorem | | ⊢ ![](../../../../number_sets/real_numbers/__pv_it/theorems/e682cd49905f8b52fcd025dd4d0c53b5fa6a75840/expr.png) |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
44 | instantiation | 51, 47, 48 | ⊢ ![](../ed2f86edfb234bf186ff915d4457a63e8d1b9b820/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/1943b60945420e340d305780feff5c1aff2740ff0/expr.png) |
45 | instantiation | 51, 52, 49 | ⊢ ![](../226944debb42acc8f970107213512ebcf205a59f0/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/682157d4892d216d9e5626ed533aff9b56b9506e0/expr.png) |
46 | instantiation | 51, 52, 50 | ⊢ ![](../bac10758646a1685ada3fe39e190d9fb360007460/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/af4aab8a07465db063742696e006d04670f30cf10/expr.png) |
47 | theorem | | ⊢ ![](../../../../number_sets/rational_numbers/__pv_it/theorems/f82654afbc103bcf8089d3e3a9860276c55562410/expr.png) |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
48 | instantiation | 51, 52, 53 | ⊢ ![](../0f3013e202906f9e4df2f20e44ea5ef8f7131b290/expr.png) |
| : , : , : ![](../../../../numerals/__pv_it/common/1943b60945420e340d305780feff5c1aff2740ff0/expr.png) |
49 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/646322292558586ba7863a63fdc6c166bd7a1aad0/expr.png) |
| proveit.numbers.numerals.decimals.nat1 |
50 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/c5da86d5508e181a625c8aa785bd1ba0345b9e710/expr.png) |
| proveit.numbers.numerals.decimals.nat2 |
51 | theorem | | ⊢ ![](../../../../../logic/sets/inclusion/__pv_it/theorems/8c2c4c3c91efdbf0b7e86e4a2d99545aea54db000/expr.png) |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
52 | theorem | | ⊢ ![](../../../../number_sets/integers/__pv_it/theorems/1cd0ce5701331e1608ae0251ff814274d551a8fa0/expr.png) |
| proveit.numbers.number_sets.integers.nat_within_int |
53 | theorem | | ⊢ ![](../../../../numerals/decimals/__pv_it/theorems/460c23cdbd64b08ccacdbdc6b3661919426e237f0/expr.png) |
| proveit.numbers.numerals.decimals.nat3 |