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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, 5, 6, 7, 8, 9, 10*, , ,  ⊢  
  : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.addition.association
2reference52  ⊢  
3reference49  ⊢  
4instantiation35  ⊢  
  : , :
5instantiation35  ⊢  
  : , :
6instantiation14, 11, 12  ⊢  
  : , :
7reference38  ⊢  
8instantiation50, 42, 13  ⊢  
  : , : , :
9instantiation14, 20, 15  ⊢  
  : , :
10instantiation16, 17, 18*  ⊢  
  : , :
11instantiation19, 29, 20, 21  ⊢  
  : , :
12instantiation50, 42, 22  ⊢  
  : , : , :
13instantiation50, 47, 23  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
15instantiation50, 42, 24  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.logic.equality.equals_reversal
17instantiation25, 26, 49, 52, 27, 28, 29, 38, 30*  ⊢  
  : , : , : , : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
19theorem  ⊢  
 proveit.numbers.division.div_complex_closure
20instantiation50, 42, 31  ⊢  
  : , : , :
21instantiation32, 33  ⊢  
  :
22instantiation50, 47, 34  ⊢  
  : , : , :
23assumption  ⊢  
24assumption  ⊢  
25theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
26axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
27theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28instantiation35  ⊢  
  : , :
29instantiation50, 42, 36  ⊢  
  : , : , :
30instantiation37, 38  ⊢  
  :
31instantiation50, 40, 39  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
33theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
34assumption  ⊢  
35theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36instantiation50, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
38instantiation50, 42, 43  ⊢  
  : , : , :
39instantiation50, 45, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation50, 45, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation50, 47, 48  ⊢  
  : , : , :
44instantiation50, 51, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation50, 51, 52  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
48assumption  ⊢  
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
50theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements