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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  ⊢  
  : , : , :
1reference50  ⊢  
2instantiation4, 71, 78, 5, 6, 7, 8, 67, 9  ⊢  
  : , : , : , : , : , :
3instantiation58, 10  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.multiplication.association
5axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
6instantiation11  ⊢  
  : , :
7theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8instantiation76, 69, 12  ⊢  
  : , : , :
9instantiation76, 69, 13  ⊢  
  : , : , :
10instantiation20, 14, 15  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12instantiation16, 17, 18  ⊢  
  : , : , :
13instantiation76, 72, 19  ⊢  
  : , : , :
14instantiation20, 21, 22  ⊢  
  : , : , :
15instantiation23, 24, 25, 26  ⊢  
  : , : , : , :
16theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
17instantiation27, 28  ⊢  
  : , :
18axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
19instantiation76, 29, 30  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
21instantiation31, 45, 32, 33  ⊢  
  : , : , : , : , :
22instantiation50, 34, 35  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
24instantiation58, 36  ⊢  
  : , : , :
25instantiation58, 36  ⊢  
  : , : , :
26instantiation61, 45  ⊢  
  :
27theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
29theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
30instantiation37, 38, 39  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
32instantiation76, 41, 40  ⊢  
  : , : , :
33instantiation76, 41, 42  ⊢  
  : , : , :
34instantiation58, 43  ⊢  
  : , : , :
35instantiation58, 44  ⊢  
  : , : , :
36instantiation60, 45  ⊢  
  :
37theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
38instantiation76, 46, 65  ⊢  
  : , : , :
39instantiation76, 46, 63  ⊢  
  : , : , :
40instantiation76, 48, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
42instantiation76, 48, 49  ⊢  
  : , : , :
43instantiation50, 51, 52  ⊢  
  : , : , :
44instantiation58, 53  ⊢  
  : , : , :
45instantiation76, 69, 54  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
47instantiation76, 56, 55  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
49instantiation76, 56, 57  ⊢  
  : , : , :
50axiom  ⊢  
 proveit.logic.equality.equals_transitivity
51instantiation58, 59  ⊢  
  : , : , :
52instantiation60, 67  ⊢  
  :
53instantiation61, 67  ⊢  
  :
54instantiation76, 72, 62  ⊢  
  : , : , :
55instantiation76, 64, 63  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57instantiation76, 64, 65  ⊢  
  : , : , :
58axiom  ⊢  
 proveit.logic.equality.substitution
59instantiation66, 67  ⊢  
  :
60theorem  ⊢  
 proveit.numbers.division.frac_one_denom
61theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
62instantiation76, 74, 68  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
64theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
65theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
66theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
67instantiation76, 69, 70  ⊢  
  : , : , :
68instantiation76, 77, 71  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
70instantiation76, 72, 73  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
72theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
73instantiation76, 74, 75  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
75instantiation76, 77, 78  ⊢  
  : , : , :
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