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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  ⊢  
  : , :
1reference12  ⊢  
2instantiation68, 49, 5  ⊢  
  : , : , :
3instantiation6, 42, 7  ⊢  
  : , :
4instantiation8, 9, 10  ⊢  
  : , : , :
5instantiation68, 57, 11  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
7instantiation12, 32, 42, 20  ⊢  
  : , :
8theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
9instantiation13, 48, 14  ⊢  
  : , :
10instantiation29, 15  ⊢  
  : , : , :
11instantiation68, 63, 16  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.division.div_complex_closure
13theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
14instantiation68, 17, 18  ⊢  
  : , : , :
15instantiation19, 32, 42, 20, 21*  ⊢  
  : , :
16instantiation68, 69, 22  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
18instantiation23, 54, 24  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.division.div_as_mult
20instantiation25, 67  ⊢  
  :
21instantiation26, 27, 28  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
23theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
24instantiation68, 66, 45  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
26axiom  ⊢  
 proveit.logic.equality.equals_transitivity
27instantiation29, 30  ⊢  
  : , : , :
28instantiation31, 32, 33  ⊢  
  : , :
29axiom  ⊢  
 proveit.logic.equality.substitution
30instantiation34, 35, 65, 36*  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.multiplication.commutation
32instantiation68, 49, 37  ⊢  
  : , : , :
33instantiation68, 49, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
35instantiation68, 39, 40  ⊢  
  : , : , :
36instantiation41, 42  ⊢  
  :
37instantiation43, 44, 45  ⊢  
  : , : , :
38instantiation68, 57, 46  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
40instantiation68, 47, 48  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
42instantiation68, 49, 50  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
44instantiation51, 52  ⊢  
  : , :
45axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
46instantiation68, 53, 54  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
48instantiation68, 55, 56  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
50instantiation68, 57, 58  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
53theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
54instantiation59, 60, 61  ⊢  
  : , :
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
56instantiation68, 62, 67  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
58instantiation68, 63, 64  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
60instantiation68, 66, 65  ⊢  
  : , : , :
61instantiation68, 66, 67  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
63theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
64instantiation68, 69, 70  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
66theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
67theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
68theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
70theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements