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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  ⊢  
  : , : , :
1reference12  ⊢  
2instantiation7, 3, 4  ⊢  
  : , : , :
3instantiation12, 5  ⊢  
  : , : , :
4instantiation14, 6  ⊢  
  : , :
5instantiation7, 8, 9  ⊢  
  : , : , :
6instantiation10, 34, 11  ⊢  
  : , :
7axiom  ⊢  
 proveit.logic.equality.equals_transitivity
8instantiation12, 13  ⊢  
  : , : , :
9instantiation14, 15  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
11instantiation16, 22, 36, 17  ⊢  
  : , :
12axiom  ⊢  
 proveit.logic.equality.substitution
13instantiation18, 51, 19, 52, 53, 20, 60, 61, 55, 22  ⊢  
  : , : , : , : , : , :
14theorem  ⊢  
 proveit.logic.equality.equals_reversal
15instantiation21, 34, 22, 23, 24, 25*, 26*  ⊢  
  : , : , : , :
16theorem  ⊢  
 proveit.numbers.division.div_complex_closure
17instantiation27, 68  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.multiplication.association
19theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
20instantiation28  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
22instantiation75, 65, 29  ⊢  
  : , : , :
23instantiation75, 31, 30  ⊢  
  : , : , :
24instantiation75, 31, 32  ⊢  
  : , : , :
25instantiation33, 34  ⊢  
  :
26instantiation35, 36  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
29instantiation75, 69, 37  ⊢  
  : , : , :
30instantiation75, 39, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
32instantiation75, 39, 40  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.division.frac_one_denom
34instantiation41, 42, 43  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
36instantiation75, 65, 44  ⊢  
  : , : , :
37instantiation75, 73, 45  ⊢  
  : , : , :
38instantiation75, 47, 46  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
40instantiation75, 47, 48  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
42instantiation59, 49, 55  ⊢  
  : , :
43instantiation50, 51, 77, 52, 53, 54, 60, 61, 55  ⊢  
  : , : , : , : , : , :
44instantiation75, 69, 56  ⊢  
  : , : , :
45assumption  ⊢  
46instantiation75, 58, 57  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
48instantiation75, 58, 68  ⊢  
  : , : , :
49instantiation59, 60, 61  ⊢  
  : , :
50theorem  ⊢  
 proveit.numbers.multiplication.disassociation
51axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
53theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
54instantiation62  ⊢  
  : , :
55theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
56instantiation75, 73, 63  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
59theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
60instantiation75, 65, 64  ⊢  
  : , : , :
61instantiation75, 65, 66  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63instantiation75, 67, 68  ⊢  
  : , : , :
64instantiation75, 69, 70  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
66instantiation75, 71, 72  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
68theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
69theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
70instantiation75, 73, 74  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
72theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
73theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
74instantiation75, 76, 77  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
77theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements