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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, 4, 5*  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_as_mult
2reference42  ⊢  
3instantiation23, 24, 32  ⊢  
  : , :
4instantiation6, 7, 8  ⊢  
  : , :
5instantiation28, 9, 10  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
7instantiation78, 11, 12  ⊢  
  : , : , :
8instantiation78, 13, 57  ⊢  
  : , : , :
9instantiation14, 15  ⊢  
  : , : , :
10instantiation16, 17  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
12instantiation78, 18, 80  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
14axiom  ⊢  
 proveit.logic.equality.substitution
15instantiation19, 24, 39, 20, 21, 22*  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
17instantiation23, 24, 25  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
19theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
20instantiation78, 59, 26  ⊢  
  : , : , :
21instantiation27, 80  ⊢  
  :
22instantiation28, 29, 30  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
24instantiation78, 54, 31  ⊢  
  : , : , :
25instantiation41, 32  ⊢  
  :
26instantiation78, 65, 33  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28axiom  ⊢  
 proveit.logic.equality.equals_transitivity
29instantiation34, 44, 56, 73, 46, 45, 47, 48, 35  ⊢  
  : , : , : , : , : , :
30instantiation36, 56, 44, 45, 46, 47, 48, 42, 37*  ⊢  
  : , : , : , : , :
31instantiation78, 59, 38  ⊢  
  : , : , :
32instantiation78, 54, 39  ⊢  
  : , : , :
33instantiation40, 66  ⊢  
  :
34theorem  ⊢  
 proveit.numbers.multiplication.disassociation
35instantiation41, 42  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
37instantiation43, 56, 44, 45, 46, 47, 48  ⊢  
  : , : , : , :
38instantiation78, 65, 49  ⊢  
  : , : , :
39instantiation78, 59, 50  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.negation.int_closure
41theorem  ⊢  
 proveit.numbers.negation.complex_closure
42instantiation78, 54, 51  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
44axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
45instantiation52  ⊢  
  : , :
46theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
47instantiation78, 54, 53  ⊢  
  : , : , :
48instantiation78, 54, 55  ⊢  
  : , : , :
49instantiation78, 72, 56  ⊢  
  : , : , :
50instantiation78, 67, 57  ⊢  
  : , : , :
51instantiation78, 59, 58  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
53instantiation78, 59, 60  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
55instantiation61, 62, 71  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
57instantiation63, 68, 64  ⊢  
  : , :
58instantiation78, 65, 66  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
60instantiation78, 67, 68  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
62instantiation69, 70  ⊢  
  : , :
63theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
64instantiation78, 79, 71  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
66instantiation78, 72, 73  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
68instantiation74, 75, 76  ⊢  
  : , :
69theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
70theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
71assumption  ⊢  
72theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
74theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
75instantiation78, 79, 77  ⊢  
  : , : , :
76instantiation78, 79, 80  ⊢  
  : , : , :
77theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
78theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
80theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements