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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  ⊢  
  : , : , :
1reference6  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 10, 59, 11*  ⊢  
  : , :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation12, 13, 28  ⊢  
  : , :
8instantiation14, 55, 53, 15, 16, 17, 28, 24, 25, 18*  ⊢  
  : , : , : , : , : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
10instantiation60, 19, 20  ⊢  
  : , : , :
11instantiation21, 22  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.multiplication.commutation
13instantiation23, 24, 25  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
15axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
16instantiation26  ⊢  
  : , :
17theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18instantiation27, 28  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20instantiation60, 29, 30  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
22instantiation60, 34, 31  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
24instantiation60, 34, 32  ⊢  
  : , : , :
25instantiation60, 34, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
28instantiation60, 34, 35  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30instantiation60, 36, 37  ⊢  
  : , : , :
31instantiation60, 43, 38  ⊢  
  : , : , :
32instantiation39, 40, 41  ⊢  
  : , : , :
33instantiation60, 43, 42  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
35instantiation60, 43, 44  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37instantiation60, 45, 62  ⊢  
  : , : , :
38instantiation60, 49, 46  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
40instantiation47, 48  ⊢  
  : , :
41assumption  ⊢  
42instantiation60, 49, 50  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
44instantiation60, 51, 52  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
46instantiation60, 54, 53  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
49theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
50instantiation60, 54, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
52instantiation56, 57, 58  ⊢  
  : , :
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
55theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
56theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
57instantiation60, 61, 59  ⊢  
  : , : , :
58instantiation60, 61, 62  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
60theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
62theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements