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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, 4, 5, 6  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.sets.enumeration.nonmembership_fold
2reference42  ⊢  
3instantiation7  ⊢  
  : , : , :
4instantiation8, 9  ⊢  
  : , :
5instantiation14, 42, 10, 11  ⊢  
  : , :
6instantiation14, 42, 12, 13  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
8theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
9instantiation14, 33, 42, 15  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
11instantiation16, 35, 17, 18, 19, 20*, 21*  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
13theorem  ⊢  
 proveit.numbers.numerals.decimals.less_3_4
14theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_nat
15theorem  ⊢  
 proveit.numbers.numerals.decimals.less_2_3
16theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
17theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
18instantiation40, 36, 22  ⊢  
  : , : , :
19instantiation23, 24  ⊢  
  :
20instantiation25, 26, 27  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_3
22instantiation40, 38, 28  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
24theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
25theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
26instantiation29, 31  ⊢  
  :
27instantiation30, 31, 32  ⊢  
  : , :
28instantiation40, 41, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
30theorem  ⊢  
 proveit.numbers.addition.commutation
31instantiation40, 34, 35  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
33theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
35instantiation40, 36, 37  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
37instantiation40, 38, 39  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
39instantiation40, 41, 42  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
*equality replacement requirements