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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.sets.enumeration.nonmembership_fold
2reference44  ⊢  
3instantiation6  ⊢  
  : , :
4instantiation7, 8  ⊢  
  : , :
5instantiation9, 10, 19  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
7theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
8instantiation12, 44, 41, 11  ⊢  
  : , :
9theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
10instantiation12, 41, 13, 14  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.less_2_3
12theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_nat
13theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
14instantiation15, 32, 16, 34, 17, 18*, 19*  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
16theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
17instantiation20, 21  ⊢  
  :
18instantiation24, 22, 23  ⊢  
  : , : , :
19instantiation24, 25, 26  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
21theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
22instantiation27, 30  ⊢  
  :
23instantiation29, 30, 28  ⊢  
  : , :
24theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
25theorem  ⊢  
 proveit.numbers.numerals.decimals.add_3_2
26instantiation29, 30, 31  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
29theorem  ⊢  
 proveit.numbers.addition.commutation
30instantiation42, 33, 32  ⊢  
  : , : , :
31instantiation42, 33, 34  ⊢  
  : , : , :
32instantiation42, 36, 35  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
34instantiation42, 36, 37  ⊢  
  : , : , :
35instantiation42, 39, 38  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
37instantiation42, 39, 40  ⊢  
  : , : , :
38instantiation42, 43, 41  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40instantiation42, 43, 44  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
42theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements