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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  ⊢  
  : , : , :
1reference12  ⊢  
2instantiation4, 33, 5, 6, 7, 8  ⊢  
  : , : , : , :
3instantiation12, 9, 10  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
5instantiation43  ⊢  
  : , : , :
6instantiation43  ⊢  
  : , : , :
7instantiation11, 53, 18  ⊢  
  : , : , :
8instantiation12, 13, 14  ⊢  
  : , : , :
9instantiation29, 73, 78, 15, 53, 42, 16  ⊢  
  : , : , : , : , : , :
10instantiation17, 36, 73, 38, 53, 42, 18  ⊢  
  : , : , : , : , : , : , : , :
11theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_12
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation19, 20  ⊢  
  : , : , :
14instantiation21, 22, 23, 24  ⊢  
  : , : , : , :
15instantiation44  ⊢  
  : , :
16instantiation59, 53  ⊢  
  :
17theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general
18instantiation25  ⊢  
  :
19axiom  ⊢  
 proveit.logic.equality.substitution
20instantiation26, 27, 60, 28*  ⊢  
  : , :
21theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
22instantiation29, 73, 78, 30, 31, 42, 54, 53  ⊢  
  : , : , : , : , : , :
23instantiation32, 36, 33, 38, 34, 42, 54, 53  ⊢  
  : , : , : , :
24instantiation35, 73, 78, 36, 37, 38, 42, 54, 53, 39*  ⊢  
  : , : , : , : , : , :
25axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
26theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
27instantiation76, 66, 40  ⊢  
  : , : , :
28instantiation41, 42  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.addition.disassociation
30instantiation44  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
32theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
33theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
34instantiation43  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.addition.association
36axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
37instantiation44  ⊢  
  : , :
38theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39instantiation45, 46, 47  ⊢  
  : , : , :
40instantiation76, 71, 48  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.negation.double_negation
42instantiation76, 66, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
44theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
46instantiation50, 53, 60, 51  ⊢  
  : , : , :
47instantiation52, 53, 54  ⊢  
  : , :
48instantiation76, 74, 55  ⊢  
  : , : , :
49instantiation56, 57, 69  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add_reversed
51theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
52theorem  ⊢  
 proveit.numbers.addition.commutation
53instantiation76, 66, 58  ⊢  
  : , : , :
54instantiation59, 60  ⊢  
  :
55instantiation61, 62  ⊢  
  :
56theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
57instantiation63, 64  ⊢  
  : , :
58instantiation76, 71, 65  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.negation.complex_closure
60instantiation76, 66, 67  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.negation.int_closure
62instantiation76, 68, 69  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
64theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
65instantiation76, 74, 70  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
67instantiation76, 71, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
69assumption  ⊢  
70instantiation76, 77, 73  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
72instantiation76, 74, 75  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
74theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
75instantiation76, 77, 78  ⊢  
  : , : , :
76theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
78theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements