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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
0generalization1  ⊢  
1instantiation2, 3, 4,  ⊢  
  : , :
2theorem  ⊢  
 proveit.numbers.multiplication.commutation
3instantiation6, 7, 5,  ⊢  
  : , :
4instantiation6, 7, 8  ⊢  
  : , :
5instantiation25, 9, 10,  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
7instantiation76, 51, 11  ⊢  
  : , : , :
8instantiation25, 12, 13  ⊢  
  : , : , :
9instantiation43, 28, 14,  ⊢  
  : , :
10instantiation19, 15, 16,  ⊢  
  : , : , :
11instantiation76, 56, 17  ⊢  
  : , : , :
12instantiation43, 28, 18  ⊢  
  : , :
13instantiation19, 20, 21  ⊢  
  : , : , :
14instantiation25, 22, 23,  ⊢  
  : , : , :
15instantiation34, 78, 29, 35, 24, 36, 28, 44, 45, 32,  ⊢  
  : , : , : , : , : , :
16instantiation34, 35, 73, 29, 36, 30, 24, 39, 40, 44, 45, 32,  ⊢  
  : , : , : , : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
18instantiation25, 26, 27  ⊢  
  : , : , :
19axiom  ⊢  
 proveit.logic.equality.equals_transitivity
20instantiation34, 78, 29, 35, 31, 36, 28, 44, 45, 38  ⊢  
  : , : , : , : , : , :
21instantiation34, 35, 73, 29, 36, 30, 31, 39, 40, 44, 45, 38  ⊢  
  : , : , : , : , : , :
22instantiation43, 33, 32,  ⊢  
  : , :
23instantiation34, 35, 73, 78, 36, 37, 44, 45, 32,  ⊢  
  : , : , : , : , : , :
24instantiation41  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
26instantiation43, 33, 38  ⊢  
  : , :
27instantiation34, 35, 73, 78, 36, 37, 44, 45, 38  ⊢  
  : , : , : , : , : , :
28instantiation43, 39, 40  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
30instantiation46  ⊢  
  : , :
31instantiation41  ⊢  
  : , : , :
32instantiation76, 51, 42,  ⊢  
  : , : , :
33instantiation43, 44, 45  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.multiplication.disassociation
35axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
36theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37instantiation46  ⊢  
  : , :
38instantiation76, 51, 47  ⊢  
  : , : , :
39instantiation76, 51, 48  ⊢  
  : , : , :
40instantiation76, 51, 49  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
42instantiation76, 54, 50,  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
45instantiation76, 51, 52  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47instantiation76, 54, 53  ⊢  
  : , : , :
48instantiation76, 54, 55  ⊢  
  : , : , :
49instantiation76, 56, 57  ⊢  
  : , : , :
50instantiation76, 59, 58,  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
52theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
53instantiation76, 59, 66  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
55instantiation76, 59, 69  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
58instantiation76, 60, 61,  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
60instantiation62, 63, 64  ⊢  
  : , :
61assumption  ⊢  
62theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
63theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
64instantiation65, 66, 67  ⊢  
  : , :
65theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
66instantiation68, 69, 70  ⊢  
  : , :
67instantiation71, 72  ⊢  
  :
68theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
69instantiation76, 77, 73  ⊢  
  : , : , :
70instantiation76, 74, 75  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.negation.int_closure
72instantiation76, 77, 78  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
74theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
75assumption  ⊢  
76theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
78theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1