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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  ⊢  
  : , : , :
1reference19  ⊢  
2instantiation4, 58, 27, 28, 7, 30, 8  ⊢  
  : , : , : , : , : , : , :
3instantiation5, 27, 60, 58, 28, 6, 7, 8, 30, 9*  ⊢  
  : , : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.addition.leftward_commutation
5theorem  ⊢  
 proveit.numbers.addition.association
6instantiation38  ⊢  
  : , :
7instantiation61, 46, 10  ⊢  
  : , : , :
8instantiation61, 46, 11  ⊢  
  : , : , :
9instantiation19, 12, 13, 14*  ⊢  
  : , : , :
10instantiation61, 50, 15  ⊢  
  : , : , :
11instantiation61, 50, 16  ⊢  
  : , : , :
12instantiation31, 17  ⊢  
  : , : , :
13instantiation24, 18  ⊢  
  : , :
14instantiation19, 20, 21  ⊢  
  : , : , :
15instantiation61, 54, 22  ⊢  
  : , : , :
16instantiation61, 54, 23  ⊢  
  : , : , :
17instantiation24, 25  ⊢  
  : , :
18instantiation26, 27, 60, 58, 28, 29, 42, 30, 37  ⊢  
  : , : , : , : , : , :
19axiom  ⊢  
 proveit.logic.equality.equals_transitivity
20instantiation31, 32  ⊢  
  : , : , :
21instantiation33, 37  ⊢  
  :
22instantiation34, 56, 52  ⊢  
  : , :
23instantiation35, 52  ⊢  
  :
24theorem  ⊢  
 proveit.logic.equality.equals_reversal
25instantiation36, 37  ⊢  
  :
26theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
27axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
28theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
29instantiation38  ⊢  
  : , :
30instantiation39, 41  ⊢  
  :
31axiom  ⊢  
 proveit.logic.equality.substitution
32instantiation40, 41, 42, 43  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
34theorem  ⊢  
 proveit.numbers.multiplication.mult_int_closure_bin
35theorem  ⊢  
 proveit.numbers.negation.int_closure
36theorem  ⊢  
 proveit.numbers.negation.mult_neg_one_left
37instantiation61, 46, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39theorem  ⊢  
 proveit.numbers.negation.complex_closure
40theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add
41instantiation61, 46, 45  ⊢  
  : , : , :
42instantiation61, 46, 47  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
44instantiation61, 50, 48  ⊢  
  : , : , :
45instantiation61, 50, 49  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation61, 50, 51  ⊢  
  : , : , :
48instantiation61, 54, 52  ⊢  
  : , : , :
49instantiation61, 54, 53  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation61, 54, 56  ⊢  
  : , : , :
52instantiation55, 56, 57  ⊢  
  : , :
53instantiation61, 59, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
55theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
56instantiation61, 59, 60  ⊢  
  : , : , :
57instantiation61, 62, 63  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
61theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
63assumption  ⊢  
*equality replacement requirements