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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,  ⊢  
  : , : , :
1reference14  ⊢  
2instantiation3, 4, 5*,  ⊢  
  :
3theorem  ⊢  
 proveit.numbers.absolute_value.complex_unit_length
4instantiation6, 7, 8,  ⊢  
  : , : , :
5instantiation9, 10,  ⊢  
  : , :
6theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
7instantiation39, 24, 11,  ⊢  
  : , :
8instantiation19, 12, 13,  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.logic.equality.equals_reversal
10instantiation14, 15,  ⊢  
  : , : , :
11instantiation39, 16, 46,  ⊢  
  : , :
12instantiation18, 75, 61, 30, 27, 32, 17, 35, 36,  ⊢  
  : , : , : , : , : , :
13instantiation18, 30, 61, 32, 26, 27, 44, 34, 35, 36,  ⊢  
  : , : , : , : , : , :
14axiom  ⊢  
 proveit.logic.equality.substitution
15instantiation19, 20, 21,  ⊢  
  : , : , :
16instantiation22, 51, 23,  ⊢  
  : , :
17instantiation76, 56, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.multiplication.disassociation
19axiom  ⊢  
 proveit.logic.equality.equals_transitivity
20instantiation25, 30, 61, 32, 26, 27, 44, 34, 33, 35, 36,  ⊢  
  : , : , : , : , : , : , :
21instantiation28, 75, 29, 30, 31, 32, 33, 44, 34, 35, 36,  ⊢  
  : , : , : , : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
23instantiation37, 38,  ⊢  
  :
24instantiation39, 51, 42  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
26instantiation40  ⊢  
  : , :
27instantiation40  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.multiplication.association
29theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
30axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
31instantiation41  ⊢  
  : , : , : , :
32theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
34instantiation76, 56, 42  ⊢  
  : , : , :
35instantiation43, 44, 45,  ⊢  
  : , :
36instantiation76, 56, 46  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.negation.nat_closure
38instantiation47, 63, 48,  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
40theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
42instantiation76, 49, 50  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
44instantiation76, 56, 51  ⊢  
  : , : , :
45instantiation52, 53,  ⊢  
  :
46theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
48instantiation54, 67, 68, 65,  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
51instantiation76, 59, 55  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.negation.complex_closure
53instantiation76, 56, 57,  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
55instantiation76, 62, 58  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
57instantiation76, 59, 60,  ⊢  
  : , : , :
58instantiation76, 74, 61  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
60instantiation76, 62, 63,  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
62theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
63instantiation76, 64, 65,  ⊢  
  : , : , :
64instantiation66, 67, 68  ⊢  
  : , :
65assumption  ⊢  
66theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
67instantiation69, 70, 71  ⊢  
  : , :
68theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
69theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
70instantiation72, 73  ⊢  
  :
71instantiation76, 74, 75  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.negation.int_closure
73instantiation76, 77, 78  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
75theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
76theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
78assumption  ⊢  
*equality replacement requirements