logo

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  ⊢  
  : , : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
2reference55  ⊢  
3axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
4theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5reference10  ⊢  
6instantiation56, 16, 8  ⊢  
  : , : , :
7instantiation9, 10, 11  ⊢  
  : , :
8instantiation12, 13, 14  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
10instantiation56, 16, 15  ⊢  
  : , : , :
11instantiation56, 16, 17  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
13instantiation18, 19  ⊢  
  :
14instantiation20, 21  ⊢  
  :
15instantiation56, 22, 23  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
17instantiation56, 30, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.negation.real_closure
19instantiation25, 26, 27  ⊢  
  : , :
20theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
21theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
24instantiation56, 32, 28  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
26instantiation56, 30, 29  ⊢  
  : , : , :
27instantiation56, 30, 31  ⊢  
  : , : , :
28instantiation52, 48  ⊢  
  :
29instantiation56, 32, 33  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
31instantiation56, 34, 35  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
33instantiation56, 36, 37  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
35instantiation38, 39, 40  ⊢  
  : , :
36instantiation41, 42, 53  ⊢  
  : , :
37assumption  ⊢  
38theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_nonzero_closure
39instantiation56, 43, 44  ⊢  
  : , : , :
40instantiation52, 45  ⊢  
  :
41theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
42instantiation46, 47, 48  ⊢  
  : , :
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
44instantiation56, 49, 50  ⊢  
  : , : , :
45instantiation56, 57, 51  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
47instantiation52, 53  ⊢  
  :
48instantiation56, 54, 55  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
50theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
51axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
52theorem  ⊢  
 proveit.numbers.negation.int_closure
53instantiation56, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
55theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
56theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
58theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos