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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  ⊢  
  : , : , :
1reference21  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation16, 6  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.logic.sets.subtraction.nonmembership_folding
5instantiation7, 8, 9  ⊢  
  : , :
6instantiation10, 11  ⊢  
  : , :
7theorem  ⊢  
 proveit.logic.booleans.disjunction.or_if_only_right
8instantiation12, 13  ⊢  
  : , :
9instantiation18, 40, 14, 15  ⊢  
  : , : , : , : , :
10theorem  ⊢  
 proveit.logic.equality.equals_reversal
11instantiation16, 17  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.logic.sets.membership.double_negated_membership
13instantiation18, 37, 19, 20  ⊢  
  : , : , : , : , :
14axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
15theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16axiom  ⊢  
 proveit.logic.equality.substitution
17instantiation21, 22, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
19instantiation24  ⊢  
  : , :
20instantiation24  ⊢  
  : , :
21theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
22theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_1
23instantiation25, 26, 27  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25theorem  ⊢  
 proveit.numbers.addition.commutation
26instantiation38, 29, 28  ⊢  
  : , : , :
27instantiation38, 29, 30  ⊢  
  : , : , :
28instantiation38, 32, 31  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
30instantiation38, 32, 33  ⊢  
  : , : , :
31instantiation38, 35, 34  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
33instantiation38, 35, 36  ⊢  
  : , : , :
34instantiation38, 39, 37  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
36instantiation38, 39, 40  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
38theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
40theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1