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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  ⊢  
  : , : , :
1reference8  ⊢  
2instantiation24, 11, 4  ⊢  
  : , :
3instantiation5, 6, 7  ⊢  
  : , : , :
4instantiation8, 9, 10  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation16, 58, 12, 17, 14, 18, 11, 25, 26, 20  ⊢  
  : , : , : , : , : , :
7instantiation16, 17, 53, 12, 18, 13, 14, 21, 22, 25, 26, 20  ⊢  
  : , : , : , : , : , :
8theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
9instantiation24, 15, 20  ⊢  
  : , :
10instantiation16, 17, 53, 58, 18, 19, 25, 26, 20  ⊢  
  : , : , : , : , : , :
11instantiation24, 21, 22  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
13instantiation27  ⊢  
  : , :
14instantiation23  ⊢  
  : , : , :
15instantiation24, 25, 26  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.multiplication.disassociation
17axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
18theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19instantiation27  ⊢  
  : , :
20instantiation56, 31, 28  ⊢  
  : , : , :
21instantiation56, 31, 29  ⊢  
  : , : , :
22instantiation56, 31, 30  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
24theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
25theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
26instantiation56, 31, 32  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28instantiation56, 34, 33  ⊢  
  : , : , :
29instantiation56, 34, 35  ⊢  
  : , : , :
30instantiation56, 36, 37  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
32theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
33instantiation56, 39, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation56, 39, 49  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
38instantiation56, 40, 41  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40instantiation42, 43, 44  ⊢  
  : , :
41assumption  ⊢  
42theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
43theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
44instantiation45, 46, 47  ⊢  
  : , :
45theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
46instantiation48, 49, 50  ⊢  
  : , :
47instantiation51, 52  ⊢  
  :
48theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
49instantiation56, 57, 53  ⊢  
  : , : , :
50instantiation56, 54, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.negation.int_closure
52instantiation56, 57, 58  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
54theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
55axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
56theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1