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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.proper_subset_of_superset
2reference59  ⊢  
3reference7  ⊢  
4instantiation10  ⊢  
  : , :
5instantiation6, 59, 7, 8, 9  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.logic.sets.enumeration.nonmembership_fold
7instantiation10  ⊢  
  : , :
8instantiation12, 11  ⊢  
  : , :
9instantiation12, 13  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11instantiation15, 58, 16, 14  ⊢  
  : , :
12theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
13instantiation15, 59, 16, 17  ⊢  
  : , :
14instantiation22, 46, 23, 18, 19, 20*, 21*  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_nat
16theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
17instantiation22, 47, 23, 49, 24, 25*, 26*  ⊢  
  : , : , :
18instantiation60, 52, 27  ⊢  
  : , : , :
19instantiation31, 28  ⊢  
  :
20instantiation35, 29, 30  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.numerals.decimals.add_4_1
22theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
24instantiation31, 32  ⊢  
  :
25instantiation35, 33, 34  ⊢  
  : , : , :
26instantiation35, 36, 37  ⊢  
  : , : , :
27instantiation60, 56, 38  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
29instantiation40, 39  ⊢  
  :
30instantiation42, 39, 41  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
32theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
33instantiation40, 43  ⊢  
  :
34instantiation42, 43, 41  ⊢  
  : , :
35theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
36theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_3
37instantiation42, 43, 44  ⊢  
  : , :
38instantiation60, 61, 45  ⊢  
  : , : , :
39instantiation60, 48, 46  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
41theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
42theorem  ⊢  
 proveit.numbers.addition.commutation
43instantiation60, 48, 47  ⊢  
  : , : , :
44instantiation60, 48, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
46instantiation60, 52, 50  ⊢  
  : , : , :
47instantiation60, 52, 51  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
49instantiation60, 52, 53  ⊢  
  : , : , :
50instantiation60, 56, 54  ⊢  
  : , : , :
51instantiation60, 56, 55  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation60, 56, 57  ⊢  
  : , : , :
54instantiation60, 61, 58  ⊢  
  : , : , :
55instantiation60, 61, 59  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
57instantiation60, 61, 62  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
60theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
*equality replacement requirements