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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.numbers.ordering.transitivity_less_less
2instantiation4, 13, 5  ⊢  
  : , : , :
3instantiation31, 6, 7  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
5instantiation8, 60, 45, 35  ⊢  
  : , : , :
6instantiation9, 10, 11, 49, 12, 13  ⊢  
  : , : , :
7instantiation14, 15, 16  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
9theorem  ⊢  
 proveit.numbers.ordering.less_eq_add_right_strong
10instantiation66, 56, 17  ⊢  
  : , : , :
11instantiation66, 56, 18  ⊢  
  : , : , :
12instantiation19, 60, 45, 35  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation20, 23, 68, 63, 25, 21, 26, 43, 42  ⊢  
  : , : , : , : , : , :
16instantiation22, 63, 68, 23, 24, 25, 26, 43, 42, 27*  ⊢  
  : , : , : , : , : , :
17instantiation66, 61, 28  ⊢  
  : , : , :
18instantiation66, 61, 45  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
20theorem  ⊢  
 proveit.numbers.addition.disassociation
21instantiation29  ⊢  
  : , :
22theorem  ⊢  
 proveit.numbers.addition.association
23axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
24instantiation29  ⊢  
  : , :
25theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26instantiation66, 50, 30  ⊢  
  : , : , :
27instantiation31, 32, 33  ⊢  
  : , : , :
28instantiation66, 34, 35  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30instantiation36, 37, 59  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
32instantiation38, 42, 39, 40  ⊢  
  : , : , :
33instantiation41, 42, 43  ⊢  
  : , :
34instantiation44, 60, 45  ⊢  
  : , :
35assumption  ⊢  
36theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
37instantiation46, 47  ⊢  
  : , :
38theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add_reversed
39instantiation66, 50, 48  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
41theorem  ⊢  
 proveit.numbers.addition.commutation
42instantiation66, 50, 49  ⊢  
  : , : , :
43instantiation66, 50, 51  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
45instantiation52, 53, 62  ⊢  
  : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
48instantiation66, 56, 54  ⊢  
  : , : , :
49instantiation66, 56, 55  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
51instantiation66, 56, 57  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
53instantiation66, 58, 59  ⊢  
  : , : , :
54instantiation66, 61, 65  ⊢  
  : , : , :
55instantiation66, 61, 60  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
57instantiation66, 61, 62  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
59theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
60instantiation66, 67, 63  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
62instantiation64, 65  ⊢  
  :
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
64theorem  ⊢  
 proveit.numbers.negation.int_closure
65instantiation66, 67, 68  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
68theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements