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_left_side_into
2instantiation4, 28, 56, 8, 5  ⊢  
  : , : , : , : , :
3instantiation6, 28, 56, 7, 8, 9  ⊢  
  : , : , : , : , : , : , :
4theorem  ⊢  
 proveit.logic.sets.enumeration.proper_subset_of_superset
5instantiation10, 11, 12  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.logic.sets.enumeration.leftward_permutation
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8instantiation20  ⊢  
  : , :
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10theorem  ⊢  
 proveit.logic.sets.inclusion.refined_nonmembership
11instantiation13, 28, 56, 14  ⊢  
  : , : , : , :
12instantiation15, 59, 16, 17, 18, 19  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.logic.sets.enumeration.subset_eq_of_superset
14instantiation20  ⊢  
  : , :
15theorem  ⊢  
 proveit.logic.sets.enumeration.nonmembership_fold
16instantiation21  ⊢  
  : , : , :
17instantiation22, 23  ⊢  
  : , :
18instantiation27, 56, 59, 24  ⊢  
  : , :
19instantiation27, 56, 25, 26  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
22theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
23instantiation27, 28, 56, 29  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.less_2_3
25theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
26instantiation30, 47, 31, 49, 32, 33*, 34*  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_nat
28theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
29theorem  ⊢  
 proveit.numbers.numerals.decimals.less_1_2
30theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
32instantiation35, 36  ⊢  
  :
33instantiation39, 37, 38  ⊢  
  : , : , :
34instantiation39, 40, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
37instantiation42, 45  ⊢  
  :
38instantiation44, 45, 43  ⊢  
  : , :
39theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
40theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_3
41instantiation44, 45, 46  ⊢  
  : , :
42theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
43theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
44theorem  ⊢  
 proveit.numbers.addition.commutation
45instantiation57, 48, 47  ⊢  
  : , : , :
46instantiation57, 48, 49  ⊢  
  : , : , :
47instantiation57, 51, 50  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
49instantiation57, 51, 52  ⊢  
  : , : , :
50instantiation57, 54, 53  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
52instantiation57, 54, 55  ⊢  
  : , : , :
53instantiation57, 58, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
55instantiation57, 58, 59  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
*equality replacement requirements