logo

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, 6, 7, 8, 9, 10, 11, 12, 13*, , ,  ⊢  
  : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.addition.association
2reference37  ⊢  
3reference82  ⊢  
4theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
5reference38  ⊢  
6instantiation64  ⊢  
  : , :
7instantiation14  ⊢  
  : , : , : , :
8reference52  ⊢  
9instantiation50, 15  ⊢  
  :
10instantiation85, 77, 16  ⊢  
  : , : , :
11instantiation85, 77, 17  ⊢  
  : , : , :
12instantiation22, 66, 18  ⊢  
  : , :
13instantiation46, 19, 20, 21*  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
15instantiation22, 51, 52  ⊢  
  : , :
16instantiation85, 71, 23  ⊢  
  : , : , :
17instantiation85, 71, 24  ⊢  
  : , : , :
18instantiation85, 77, 25  ⊢  
  : , : , :
19instantiation26, 27  ⊢  
  : , : , :
20instantiation34, 28  ⊢  
  : , :
21instantiation29, 84, 30, 79, 31*, 32*, 33*  ⊢  
  : , : , : , :
22theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
23assumption  ⊢  
24assumption  ⊢  
25assumption  ⊢  
26axiom  ⊢  
 proveit.logic.equality.substitution
27instantiation34, 35  ⊢  
  : , :
28instantiation36, 37, 82, 87, 38, 39, 75, 40, 52, 41*  ⊢  
  : , : , : , : , : , :
29theorem  ⊢  
 proveit.numbers.addition.rational_pair_addition
30instantiation42, 84  ⊢  
  :
31instantiation43, 75, 44  ⊢  
  :
32instantiation45, 75, 66, 62  ⊢  
  : , :
33instantiation46, 47, 48  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.logic.equality.equals_reversal
35instantiation49, 51, 52  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
37axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
38theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39instantiation64  ⊢  
  : , :
40instantiation50, 51  ⊢  
  :
41instantiation65, 52  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.negation.int_closure
43theorem  ⊢  
 proveit.numbers.division.frac_cancel_complete
44instantiation69, 53  ⊢  
  :
45theorem  ⊢  
 proveit.numbers.division.neg_frac_neg_numerator
46axiom  ⊢  
 proveit.logic.equality.equals_transitivity
47instantiation54, 82, 55, 56, 57, 58  ⊢  
  : , : , : , :
48instantiation59, 75, 66, 60  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.negation.neg_times_pos
50theorem  ⊢  
 proveit.numbers.negation.complex_closure
51instantiation61, 75, 66, 62  ⊢  
  : , :
52instantiation85, 77, 63  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
54axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
55instantiation64  ⊢  
  : , :
56instantiation64  ⊢  
  : , :
57instantiation65, 66  ⊢  
  :
58instantiation67, 75, 68*  ⊢  
  : , :
59theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add
60theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
61theorem  ⊢  
 proveit.numbers.division.div_complex_closure
62instantiation69, 70  ⊢  
  :
63instantiation85, 71, 72  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
65theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
66instantiation85, 77, 73  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.negation.pos_times_neg
68instantiation74, 75  ⊢  
  :
69theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
70theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
71theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
72assumption  ⊢  
73instantiation85, 80, 76  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
75instantiation85, 77, 78  ⊢  
  : , : , :
76instantiation85, 83, 79  ⊢  
  : , : , :
77theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
78instantiation85, 80, 81  ⊢  
  : , : , :
79instantiation85, 86, 82  ⊢  
  : , : , :
80theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
81instantiation85, 83, 84  ⊢  
  : , : , :
82theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
83theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
84instantiation85, 86, 87  ⊢  
  : , : , :
85theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
86theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
87theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements