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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
2instantiation60, 14, 4  ⊢  
  : , : , :
3instantiation5, 6, 32, 59, 7, 8, 9, 10, 11  ⊢  
  : , : , : , : , : , :
4instantiation29, 12, 15  ⊢  
  : , :
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
8instantiation13  ⊢  
  : , :
9instantiation60, 14, 16  ⊢  
  : , : , :
10instantiation60, 14, 17  ⊢  
  : , : , :
11instantiation60, 14, 15  ⊢  
  : , : , :
12instantiation29, 16, 17  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
15instantiation18, 19, 20  ⊢  
  : , :
16instantiation60, 34, 21  ⊢  
  : , : , :
17instantiation60, 22, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
19instantiation24, 25  ⊢  
  :
20instantiation26, 27  ⊢  
  :
21instantiation60, 36, 28  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
24theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
25theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
26theorem  ⊢  
 proveit.numbers.negation.real_closure
27instantiation29, 30, 31  ⊢  
  : , :
28instantiation60, 58, 32  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
30instantiation60, 34, 33  ⊢  
  : , : , :
31instantiation60, 34, 35  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
33instantiation60, 36, 37  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation60, 38, 39  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
37instantiation60, 40, 41  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
39instantiation42, 43, 44  ⊢  
  : , :
40instantiation45, 46, 57  ⊢  
  : , :
41assumption  ⊢  
42theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_nonzero_closure
43instantiation60, 47, 48  ⊢  
  : , : , :
44instantiation56, 49  ⊢  
  :
45theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
46instantiation50, 51, 52  ⊢  
  : , :
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
48instantiation60, 53, 54  ⊢  
  : , : , :
49instantiation60, 61, 55  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
51instantiation56, 57  ⊢  
  :
52instantiation60, 58, 59  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
55axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
56theorem  ⊢  
 proveit.numbers.negation.int_closure
57instantiation60, 61, 62  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
60theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
62theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos