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  ⊢  
  : , : , :
1reference26  ⊢  
2instantiation4, 5, 6, 44, 7, 8  ⊢  
  : , : , :
3instantiation9, 10, 11  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.ordering.less_eq_add_right_strong
5instantiation61, 51, 12  ⊢  
  : , : , :
6instantiation61, 51, 13  ⊢  
  : , : , :
7instantiation14, 55, 40, 30  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
9axiom  ⊢  
 proveit.logic.equality.equals_transitivity
10instantiation15, 18, 63, 58, 20, 16, 21, 38, 37  ⊢  
  : , : , : , : , : , :
11instantiation17, 58, 63, 18, 19, 20, 21, 38, 37, 22*  ⊢  
  : , : , : , : , : , :
12instantiation61, 56, 23  ⊢  
  : , : , :
13instantiation61, 56, 40  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
15theorem  ⊢  
 proveit.numbers.addition.disassociation
16instantiation24  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.addition.association
18axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
19instantiation24  ⊢  
  : , :
20theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
21instantiation61, 45, 25  ⊢  
  : , : , :
22instantiation26, 27, 28  ⊢  
  : , : , :
23instantiation61, 29, 30  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25instantiation31, 32, 54  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
27instantiation33, 37, 34, 35  ⊢  
  : , : , :
28instantiation36, 37, 38  ⊢  
  : , :
29instantiation39, 55, 40  ⊢  
  : , :
30assumption  ⊢  
31theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
32instantiation41, 42  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add_reversed
34instantiation61, 45, 43  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
36theorem  ⊢  
 proveit.numbers.addition.commutation
37instantiation61, 45, 44  ⊢  
  : , : , :
38instantiation61, 45, 46  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
40instantiation47, 48, 57  ⊢  
  : , :
41theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
43instantiation61, 51, 49  ⊢  
  : , : , :
44instantiation61, 51, 50  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
46instantiation61, 51, 52  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
48instantiation61, 53, 54  ⊢  
  : , : , :
49instantiation61, 56, 60  ⊢  
  : , : , :
50instantiation61, 56, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
52instantiation61, 56, 57  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
54theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
55instantiation61, 62, 58  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
57instantiation59, 60  ⊢  
  :
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
59theorem  ⊢  
 proveit.numbers.negation.int_closure
60instantiation61, 62, 63  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements