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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 7, 58, 53, 9, 5, 10, 26, 28  ⊢  
  : , : , : , : , : , :
3instantiation6, 53, 58, 7, 8, 9, 10, 26, 28, 11*  ⊢  
  : , : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.addition.disassociation
5instantiation12  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.addition.association
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8instantiation12  ⊢  
  : , :
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10instantiation13, 14, 15  ⊢  
  : , :
11instantiation16, 17, 18  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
14instantiation19, 28, 20, 21  ⊢  
  : , :
15instantiation27, 38, 22  ⊢  
  : , :
16theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
17instantiation23, 28, 38, 24  ⊢  
  : , : , :
18instantiation25, 28, 26  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.division.div_complex_closure
20instantiation27, 38, 28  ⊢  
  : , :
21instantiation29, 30, 31  ⊢  
  : , : , :
22instantiation56, 44, 32  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add_reversed
24theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
25theorem  ⊢  
 proveit.numbers.addition.commutation
26instantiation56, 44, 33  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
28instantiation56, 44, 34  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
30instantiation35, 36  ⊢  
  :
31instantiation37, 38  ⊢  
  :
32instantiation39, 40, 41  ⊢  
  : , : , :
33instantiation56, 50, 42  ⊢  
  : , : , :
34instantiation56, 50, 43  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
36theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
37theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
38instantiation56, 44, 45  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
40instantiation46, 47  ⊢  
  : , :
41axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
42instantiation56, 54, 48  ⊢  
  : , : , :
43instantiation56, 54, 49  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
45instantiation56, 50, 51  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
48instantiation52, 55  ⊢  
  :
49instantiation56, 57, 53  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation56, 54, 55  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.negation.int_closure
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
54theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
55instantiation56, 57, 58  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements