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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, 34, 5, 6, 7, 8  ⊢  
  : , : , : , :
3instantiation12, 9, 10  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
5instantiation44  ⊢  
  : , : , :
6instantiation44  ⊢  
  : , : , :
7instantiation11, 46, 39  ⊢  
  : , : , :
8instantiation12, 13, 14  ⊢  
  : , : , :
9instantiation15, 67, 33, 35, 46, 42  ⊢  
  : , : , : , : , : , : , :
10instantiation16, 33, 29, 67, 35, 17, 46, 42, 18*  ⊢  
  : , : , : , : , : , :
11theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_12
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation19, 20  ⊢  
  : , : , :
14instantiation21, 22, 23, 24  ⊢  
  : , : , : , :
15theorem  ⊢  
 proveit.numbers.addition.leftward_commutation
16theorem  ⊢  
 proveit.numbers.addition.association
17instantiation43  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
19axiom  ⊢  
 proveit.logic.equality.substitution
20instantiation25, 26, 46, 27*  ⊢  
  : , :
21theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
22instantiation28, 67, 29, 30, 31, 42, 37, 46  ⊢  
  : , : , : , : , : , :
23instantiation32, 33, 34, 35, 36, 42, 37, 46  ⊢  
  : , : , : , :
24instantiation38, 46, 42, 39  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
26instantiation65, 50, 40  ⊢  
  : , : , :
27instantiation41, 42  ⊢  
  :
28theorem  ⊢  
 proveit.numbers.addition.disassociation
29theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
30instantiation43  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
32theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
33axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
34theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
35theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36instantiation44  ⊢  
  : , : , :
37instantiation45, 46  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_32
39instantiation47  ⊢  
  :
40instantiation65, 55, 48  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.negation.double_negation
42instantiation65, 50, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
45theorem  ⊢  
 proveit.numbers.negation.complex_closure
46instantiation65, 50, 51  ⊢  
  : , : , :
47axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
48instantiation65, 61, 52  ⊢  
  : , : , :
49instantiation53, 54, 64  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
51instantiation65, 55, 56  ⊢  
  : , : , :
52instantiation57, 58  ⊢  
  :
53theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
54instantiation59, 60  ⊢  
  : , :
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
56instantiation65, 61, 62  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.negation.int_closure
58instantiation65, 63, 64  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
61theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
62instantiation65, 66, 67  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
64assumption  ⊢  
65theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
67theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements