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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
2instantiation7, 4  ⊢  
  : , : , :
3instantiation5, 10, 11, 12, 13, 17, 14, 15, 6*  ⊢  
  : , : , : , : , :
4instantiation7, 8  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
6instantiation9, 10, 11, 12, 13, 14, 15  ⊢  
  : , : , : , :
7axiom  ⊢  
 proveit.logic.equality.substitution
8instantiation16, 17, 24, 18*  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
10axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
11theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
12theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13instantiation19  ⊢  
  : , :
14instantiation59, 29, 20  ⊢  
  : , : , :
15instantiation59, 29, 21  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_left
17instantiation59, 29, 22  ⊢  
  : , : , :
18instantiation23, 24  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20instantiation59, 27, 25  ⊢  
  : , : , :
21instantiation59, 27, 26  ⊢  
  : , : , :
22instantiation59, 27, 28  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
24instantiation59, 29, 30  ⊢  
  : , : , :
25instantiation59, 34, 31  ⊢  
  : , : , :
26instantiation59, 32, 33  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
28instantiation59, 34, 51  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
30instantiation35, 36, 54  ⊢  
  : , : , :
31instantiation59, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
33instantiation39, 40, 41  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
35theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
36instantiation42, 43  ⊢  
  : , :
37instantiation44, 45, 56  ⊢  
  : , :
38assumption  ⊢  
39theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_nonzero_closure
40instantiation59, 46, 47  ⊢  
  : , : , :
41instantiation55, 48  ⊢  
  :
42theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
44theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
45instantiation49, 50, 51  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
47instantiation59, 52, 53  ⊢  
  : , : , :
48instantiation59, 60, 54  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
50instantiation55, 56  ⊢  
  :
51instantiation59, 57, 58  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
54axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
55theorem  ⊢  
 proveit.numbers.negation.int_closure
56instantiation59, 60, 61  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
59theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
61theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements