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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, , ,  ⊢  
  : , : , :
1reference50  ⊢  
2instantiation4, 73, 14, 13, 5, 15, 66, 18, 17, , ,  ⊢  
  : , : , : , : , : , :
3instantiation50, 6, 7, , ,  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.multiplication.disassociation
5instantiation20  ⊢  
  : , :
6instantiation8, 13, 14, 15, 9, 66, 18, 17, , ,  ⊢  
  : , : , : , : , : , : , :
7instantiation50, 10, 11, , ,  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
9instantiation20  ⊢  
  : , :
10instantiation12, 13, 14, 73, 15, 16, 17, 66, 18, , ,  ⊢  
  : , : , : , : , : , :
11instantiation58, 19, ,  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.multiplication.association
13axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
14theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
15theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16instantiation20  ⊢  
  : , :
17instantiation21, 45, 66, 42, ,  ⊢  
  : , :
18instantiation71, 69, 22  ⊢  
  : , : , :
19instantiation25, 23, 24, ,  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21theorem  ⊢  
 proveit.numbers.division.div_complex_closure
22assumption  ⊢  
23instantiation25, 26, 27, ,  ⊢  
  : , : , :
24instantiation28, 29, 30, 31  ⊢  
  : , : , : , :
25theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
26instantiation32, 45, 46, 33, 34, ,  ⊢  
  : , : , : , : , :
27instantiation50, 35, 36  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
29instantiation58, 37  ⊢  
  : , : , :
30instantiation58, 38  ⊢  
  : , : , :
31instantiation65, 45  ⊢  
  :
32theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
33instantiation71, 39, 40  ⊢  
  : , : , :
34instantiation41, 66, 42,  ⊢  
  :
35instantiation58, 43  ⊢  
  : , : , :
36instantiation58, 44  ⊢  
  : , : , :
37instantiation60, 45  ⊢  
  :
38instantiation60, 46  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
40instantiation71, 47, 48  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
42assumption  ⊢  
43instantiation58, 49  ⊢  
  : , : , :
44instantiation50, 51, 52  ⊢  
  : , : , :
45instantiation71, 69, 53  ⊢  
  : , : , :
46instantiation71, 69, 54  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
48instantiation71, 55, 56  ⊢  
  : , : , :
49instantiation57, 66  ⊢  
  :
50axiom  ⊢  
 proveit.logic.equality.equals_transitivity
51instantiation58, 59  ⊢  
  : , : , :
52instantiation60, 66  ⊢  
  :
53assumption  ⊢  
54instantiation71, 61, 62  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
56instantiation71, 63, 64  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
58axiom  ⊢  
 proveit.logic.equality.substitution
59instantiation65, 66  ⊢  
  :
60theorem  ⊢  
 proveit.numbers.division.frac_one_denom
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
62instantiation71, 67, 68  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
64theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
65theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
66instantiation71, 69, 70  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
68instantiation71, 72, 73  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
70assumption  ⊢  
71theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1