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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.multiplication.disassociation
2theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
3reference45  ⊢  
4axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
5instantiation11  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7instantiation12, 13, 14  ⊢  
  : , :
8instantiation46, 32, 15  ⊢  
  : , : , :
9instantiation46, 32, 16  ⊢  
  : , : , :
10instantiation46, 32, 17  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
12theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
13instantiation18, 19, 20, 21  ⊢  
  : , :
14instantiation22, 23, 24  ⊢  
  : , :
15instantiation46, 36, 25  ⊢  
  : , : , :
16instantiation46, 36, 26  ⊢  
  : , : , :
17assumption  ⊢  
18theorem  ⊢  
 proveit.numbers.division.div_complex_closure
19instantiation46, 32, 27  ⊢  
  : , : , :
20instantiation46, 32, 28  ⊢  
  : , : , :
21instantiation29, 30  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
23instantiation46, 32, 31  ⊢  
  : , : , :
24instantiation46, 32, 33  ⊢  
  : , : , :
25assumption  ⊢  
26assumption  ⊢  
27instantiation46, 38, 34  ⊢  
  : , : , :
28instantiation46, 38, 35  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
31instantiation46, 36, 37  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation46, 38, 39  ⊢  
  : , : , :
34instantiation46, 42, 40  ⊢  
  : , : , :
35instantiation46, 42, 41  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
37assumption  ⊢  
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation46, 42, 43  ⊢  
  : , : , :
40instantiation46, 47, 44  ⊢  
  : , : , :
41instantiation46, 47, 45  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
43instantiation46, 47, 48  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2