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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
2instantiation29, 4, 16  ⊢  
  : , :
3instantiation5, 6, 28, 58, 7, 8, 9, 10, 11  ⊢  
  : , : , : , : , : , :
4instantiation29, 13, 14  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.multiplication.disassociation
6axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
7theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8instantiation12  ⊢  
  : , :
9instantiation59, 15, 13  ⊢  
  : , : , :
10instantiation59, 15, 14  ⊢  
  : , : , :
11instantiation59, 15, 16  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13instantiation59, 33, 17  ⊢  
  : , : , :
14instantiation59, 18, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
16instantiation20, 21, 22  ⊢  
  : , :
17instantiation59, 35, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
19theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
20theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
21instantiation24, 25  ⊢  
  :
22instantiation26, 27  ⊢  
  :
23instantiation59, 57, 28  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.negation.real_closure
25instantiation29, 30, 31  ⊢  
  : , :
26theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
27theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
28theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
29theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
30instantiation59, 33, 32  ⊢  
  : , : , :
31instantiation59, 33, 34  ⊢  
  : , : , :
32instantiation59, 35, 36  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
34instantiation59, 37, 38  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
36instantiation59, 39, 40  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
38instantiation41, 42, 43  ⊢  
  : , :
39instantiation44, 45, 56  ⊢  
  : , :
40assumption  ⊢  
41theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_nonzero_closure
42instantiation59, 46, 47  ⊢  
  : , : , :
43instantiation55, 48  ⊢  
  :
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