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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, 45, 8, 7, 10, 9, 5, 11, 12  ⊢  
  : , : , : , : , : , :
3instantiation6, 7, 8, 9, 10, 11, 12  ⊢  
  : , : , : , :
4theorem  ⊢  
 proveit.numbers.multiplication.disassociation
5instantiation46, 16, 13  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10instantiation14  ⊢  
  : , :
11instantiation46, 16, 15  ⊢  
  : , : , :
12instantiation46, 16, 17  ⊢  
  : , : , :
13instantiation46, 20, 18  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15instantiation46, 20, 19  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
17instantiation46, 20, 21  ⊢  
  : , : , :
18instantiation46, 22, 38  ⊢  
  : , : , :
19instantiation46, 22, 23  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
21instantiation46, 24, 25  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
23instantiation46, 26, 27  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
25instantiation28, 29, 30  ⊢  
  : , :
26instantiation31, 32, 43  ⊢  
  : , :
27assumption  ⊢  
28theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_nonzero_closure
29instantiation46, 33, 34  ⊢  
  : , : , :
30instantiation42, 35  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
32instantiation36, 37, 38  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
34instantiation46, 39, 40  ⊢  
  : , : , :
35instantiation46, 47, 41  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
37instantiation42, 43  ⊢  
  :
38instantiation46, 44, 45  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
40theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
41axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
42theorem  ⊢  
 proveit.numbers.negation.int_closure
43instantiation46, 47, 48  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
48theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos