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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, 18, 57, 52, 19, 5, 8, 35, 6  ⊢  
  : , : , : , : , : , :
3instantiation7, 35, 8, 9  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.addition.disassociation
5instantiation25  ⊢  
  : , :
6instantiation55, 47, 10  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
8instantiation11, 12, 13  ⊢  
  : , : , :
9instantiation14  ⊢  
  :
10instantiation55, 50, 15  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
12instantiation23, 16, 21  ⊢  
  : , :
13instantiation17, 18, 57, 52, 19, 20, 45, 24, 21  ⊢  
  : , : , : , : , : , :
14axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
15instantiation55, 53, 22  ⊢  
  : , : , :
16instantiation23, 45, 24  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.multiplication.disassociation
18axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
19theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20instantiation25  ⊢  
  : , :
21instantiation55, 47, 26  ⊢  
  : , : , :
22instantiation27, 49  ⊢  
  :
23theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
24instantiation28, 35, 29, 30  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
26instantiation31, 32, 33  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.negation.int_closure
28theorem  ⊢  
 proveit.numbers.division.div_complex_closure
29instantiation34, 45, 35  ⊢  
  : , :
30instantiation36, 37, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
32instantiation39, 40  ⊢  
  : , :
33theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
34theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
35instantiation55, 47, 41  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
37instantiation42, 43  ⊢  
  :
38instantiation44, 45  ⊢  
  :
39theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
41instantiation55, 50, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
44theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
45instantiation55, 47, 48  ⊢  
  : , : , :
46instantiation55, 53, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
48instantiation55, 50, 51  ⊢  
  : , : , :
49instantiation55, 56, 52  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation55, 53, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
53theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
54instantiation55, 56, 57  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2