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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, , , , ,  ⊢  
  : , : , : , :
1reference5  ⊢  
2instantiation5, 6, 7, 8, , , , ,  ⊢  
  : , : , : , :
3instantiation31, 46, 65, 9, 48, 10, 11, 50, 32, 24, 60, 25, 26, 27, 28, 12*, , , , ,  ⊢  
  : , : , : , : , : , :
4instantiation31, 47, 21, 13, 14, 23, 15, 24, 60, 25, 26, 27, 28, 16*, , , , ,  ⊢  
  : , : , : , : , : , :
5theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
6instantiation20, 70, 18, 47, 19, 17, 50, 24, 60, 25, 26, 27, 28, 32, , , , ,  ⊢  
  : , : , : , : , : , : , :
7instantiation20, 47, 18, 70, 49, 19, 50, 24, 60, 25, 26, 27, 28, 32, , , , ,  ⊢  
  : , : , : , : , : , : , :
8instantiation20, 62, 21, 46, 22, 23, 48, 50, 32, 24, 60, 25, 26, 27, 28, , , , ,  ⊢  
  : , : , : , : , : , : , :
9theorem  ⊢  
 proveit.numbers.numerals.decimals.nat7
10instantiation29  ⊢  
  : , : , :
11instantiation30  ⊢  
  : , : , : , : , : , : , :
12instantiation31, 46, 47, 70, 48, 49, 50, 32, 33*  ⊢  
  : , : , : , : , : , :
13instantiation56  ⊢  
  : , :
14instantiation56  ⊢  
  : , :
15instantiation68, 57, 34  ⊢  
  : , : , :
16instantiation35, 36, 54*  ⊢  
  : , :
17instantiation56  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.nat6
19instantiation37  ⊢  
  : , : , : , : , : , :
20theorem  ⊢  
 proveit.numbers.addition.leftward_commutation
21theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
22instantiation38  ⊢  
  : , : , : , : , :
23instantiation39  ⊢  
  : , : , : , :
24assumption  ⊢  
25assumption  ⊢  
26assumption  ⊢  
27assumption  ⊢  
28assumption  ⊢  
29theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
30theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
31theorem  ⊢  
 proveit.numbers.addition.association
32instantiation68, 57, 40  ⊢  
  : , : , :
33instantiation41, 42, 43  ⊢  
  : , : , :
34instantiation68, 63, 44  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.logic.equality.equals_reversal
36instantiation45, 46, 47, 70, 48, 49, 50, 60, 51*  ⊢  
  : , : , : , : , : , :
37theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
38theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
39theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
40instantiation68, 63, 52  ⊢  
  : , : , :
41axiom  ⊢  
 proveit.logic.equality.equals_transitivity
42instantiation53, 54  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_3
44instantiation68, 66, 55  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
46axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
48theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49instantiation56  ⊢  
  : , :
50instantiation68, 57, 58  ⊢  
  : , : , :
51instantiation59, 60  ⊢  
  :
52instantiation68, 66, 61  ⊢  
  : , : , :
53axiom  ⊢  
 proveit.logic.equality.substitution
54theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
55instantiation68, 69, 62  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
57theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
58instantiation68, 63, 64  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
60assumption  ⊢  
61instantiation68, 69, 65  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
63theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
64instantiation68, 66, 67  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
66theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
67instantiation68, 69, 70  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
70theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements