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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 7, 46, 53, 9, 5, 10, 22, 21  ⊢  
  : , : , : , : , : , :
3instantiation6, 53, 46, 7, 8, 9, 10, 22, 21, 11*  ⊢  
  : , : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.addition.disassociation
5instantiation12  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.addition.association
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8instantiation12  ⊢  
  : , :
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10instantiation44, 30, 13  ⊢  
  : , : , :
11instantiation14, 15, 16  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13instantiation44, 35, 17  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
15instantiation18, 21, 26, 19  ⊢  
  : , : , :
16instantiation20, 21, 22  ⊢  
  : , :
17instantiation44, 39, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add_reversed
19theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
20theorem  ⊢  
 proveit.numbers.addition.commutation
21instantiation44, 30, 24  ⊢  
  : , : , :
22instantiation25, 26  ⊢  
  :
23instantiation44, 27, 28  ⊢  
  : , : , :
24instantiation44, 35, 29  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.negation.complex_closure
26instantiation44, 30, 31  ⊢  
  : , : , :
27instantiation32, 40, 33  ⊢  
  : , :
28assumption  ⊢  
29instantiation44, 39, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
31instantiation44, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
33instantiation44, 37, 38  ⊢  
  : , : , :
34instantiation44, 45, 53  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
36instantiation44, 39, 40  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
38instantiation41, 53, 42, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40instantiation44, 45, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
42instantiation47, 53, 48  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
44theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
47theorem  ⊢  
 proveit.numbers.numerals.decimals.n_in_digits
48instantiation49, 50, 51  ⊢  
  : , :
49theorem  ⊢  
 proveit.logic.booleans.conjunction.and_if_both
50instantiation52, 53  ⊢  
  :
51instantiation54, 55  ⊢  
  :
52theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_lower_bound
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
54theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
55theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat9
*equality replacement requirements