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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, 4, 5, 6, 7, 8, 9  ⊢  
  : , : , : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general
2axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
3reference61  ⊢  
4theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5instantiation10  ⊢  
  : , :
6instantiation59, 46, 11  ⊢  
  : , : , :
7instantiation12, 13  ⊢  
  :
8reference27  ⊢  
9instantiation14  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11instantiation59, 54, 15  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.negation.complex_closure
13instantiation16, 17, 18  ⊢  
  : , :
14axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
15instantiation59, 57, 19  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
17instantiation20, 27, 21, 22  ⊢  
  : , :
18instantiation26, 38, 23  ⊢  
  : , :
19instantiation59, 24, 25  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.division.div_complex_closure
21instantiation26, 38, 27  ⊢  
  : , :
22instantiation28, 29, 30  ⊢  
  : , : , :
23instantiation59, 46, 31  ⊢  
  : , : , :
24instantiation32, 53, 33  ⊢  
  : , :
25assumption  ⊢  
26theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
27instantiation59, 46, 34  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
29instantiation35, 36  ⊢  
  :
30instantiation37, 38  ⊢  
  :
31instantiation39, 40, 41  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
33instantiation42, 43, 44  ⊢  
  : , :
34instantiation59, 54, 45  ⊢  
  : , : , :
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
38instantiation59, 46, 47  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
40instantiation48, 49  ⊢  
  : , :
41axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
42theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
43instantiation59, 50, 51  ⊢  
  : , : , :
44instantiation52, 58  ⊢  
  :
45instantiation59, 57, 53  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation59, 54, 55  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
51theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
52theorem  ⊢  
 proveit.numbers.negation.int_closure
53instantiation59, 60, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
55instantiation59, 57, 58  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
57theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
58instantiation59, 60, 61  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
61theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2