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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
2instantiation4, 37, 5  ⊢  
  : , :
3instantiation18, 6  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
5instantiation57, 7, 8  ⊢  
  : , : , :
6instantiation9, 21, 31, 10, 11*  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
8instantiation12, 43, 13  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.division.div_as_mult
10instantiation14, 56  ⊢  
  :
11instantiation15, 16, 17  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
13instantiation57, 55, 34  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
15axiom  ⊢  
 proveit.logic.equality.equals_transitivity
16instantiation18, 19  ⊢  
  : , : , :
17instantiation20, 21, 22  ⊢  
  : , :
18axiom  ⊢  
 proveit.logic.equality.substitution
19instantiation23, 24, 54, 25*  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.multiplication.commutation
21instantiation57, 38, 26  ⊢  
  : , : , :
22instantiation57, 38, 27  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
24instantiation57, 28, 29  ⊢  
  : , : , :
25instantiation30, 31  ⊢  
  :
26instantiation32, 33, 34  ⊢  
  : , : , :
27instantiation57, 46, 35  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
29instantiation57, 36, 37  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
31instantiation57, 38, 39  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
33instantiation40, 41  ⊢  
  : , :
34axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
35instantiation57, 42, 43  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
37instantiation57, 44, 45  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
39instantiation57, 46, 47  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
43instantiation48, 49, 50  ⊢  
  : , :
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
45instantiation57, 51, 56  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
47instantiation57, 52, 53  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
49instantiation57, 55, 54  ⊢  
  : , : , :
50instantiation57, 55, 56  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
52theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
53instantiation57, 58, 59  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
56theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements