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Show the Proof

In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0instantiation1, 2, 3, ,  ⊢  
  : , : , :
1reference29  ⊢  
2instantiation4, 62, 78, 5, 47, 13, 14, 12, 15, ,  ⊢  
  : , : , : , : , : , : , :
3instantiation6, 7, 78, 8, 9, 10, 11, 47, 12, 13, 14, 15, 16*, ,  ⊢  
  : , : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
5instantiation46  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.multiplication.association
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10instantiation46  ⊢  
  : , :
11instantiation17  ⊢  
  : , : , :
12instantiation18, 24, 54, 19  ⊢  
  : , :
13assumption  ⊢  
14assumption  ⊢  
15instantiation20, 21, 22  ⊢  
  : , :
16instantiation23, 47, 24, 41, 40, 25*, 26*  ⊢  
  : , : , : , :
17theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18theorem  ⊢  
 proveit.numbers.division.div_complex_closure
19instantiation27, 70  ⊢  
  :
20theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
21assumption  ⊢  
22instantiation76, 60, 28  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
24instantiation76, 60, 33  ⊢  
  : , : , :
25instantiation53, 47  ⊢  
  :
26instantiation29, 30, 31  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28instantiation32, 33  ⊢  
  :
29axiom  ⊢  
 proveit.logic.equality.equals_transitivity
30instantiation34, 78, 35, 36, 37, 38  ⊢  
  : , : , : , :
31instantiation39, 40, 41, 54, 42*, 43*, 44*  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.negation.real_closure
33instantiation76, 67, 45  ⊢  
  : , : , :
34axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
35instantiation46  ⊢  
  : , :
36instantiation46  ⊢  
  : , :
37instantiation52, 47  ⊢  
  :
38instantiation48, 54  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
40instantiation76, 50, 49  ⊢  
  : , : , :
41instantiation76, 50, 51  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
43instantiation52, 54  ⊢  
  :
44instantiation53, 54  ⊢  
  :
45instantiation76, 73, 55  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47instantiation76, 60, 56  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
49instantiation76, 58, 57  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
51instantiation76, 58, 59  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
53theorem  ⊢  
 proveit.numbers.division.frac_one_denom
54instantiation76, 60, 61  ⊢  
  : , : , :
55instantiation76, 77, 62  ⊢  
  : , : , :
56instantiation76, 67, 63  ⊢  
  : , : , :
57instantiation76, 65, 64  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
59instantiation76, 65, 66  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
61instantiation76, 67, 68  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
63instantiation76, 73, 69  ⊢  
  : , : , :
64instantiation76, 71, 70  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
66instantiation76, 71, 72  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
68instantiation76, 73, 74  ⊢  
  : , : , :
69instantiation76, 77, 75  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
72theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
73theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
74instantiation76, 77, 78  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
76theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
78theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements