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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 10, 40, 11*  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.multiplication.commutation
7instantiation43, 24, 12  ⊢  
  : , : , :
8instantiation43, 24, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
10instantiation43, 14, 15  ⊢  
  : , : , :
11instantiation16, 17  ⊢  
  :
12instantiation18, 19, 20  ⊢  
  : , : , :
13instantiation43, 32, 21  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
15instantiation43, 22, 23  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
17instantiation43, 24, 25  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
19instantiation26, 27  ⊢  
  : , :
20axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
21instantiation43, 28, 29  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
23instantiation43, 30, 31  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
25instantiation43, 32, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
28theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
29instantiation34, 35, 36  ⊢  
  : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
31instantiation43, 37, 42  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
33instantiation43, 38, 39  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
35instantiation43, 41, 40  ⊢  
  : , : , :
36instantiation43, 41, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
39instantiation43, 44, 45  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
42theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
43theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements