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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  ⊢  
  : , : , :
1reference36  ⊢  
2instantiation5, 3, 4  ⊢  
  : , : , :
3instantiation5, 6, 7  ⊢  
  : , : , :
4instantiation8, 9, 10, 11  ⊢  
  : , : , : , :
5theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
6instantiation12, 23, 13, 14  ⊢  
  : , : , : , : , :
7instantiation28, 15, 16  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
9instantiation36, 17  ⊢  
  : , : , :
10instantiation36, 17  ⊢  
  : , : , :
11instantiation43, 23  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
13instantiation49, 19, 18  ⊢  
  : , : , :
14instantiation49, 19, 20  ⊢  
  : , : , :
15instantiation36, 21  ⊢  
  : , : , :
16instantiation36, 22  ⊢  
  : , : , :
17instantiation38, 23  ⊢  
  :
18instantiation49, 25, 24  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20instantiation49, 25, 26  ⊢  
  : , : , :
21instantiation36, 27  ⊢  
  : , : , :
22instantiation28, 29, 30  ⊢  
  : , : , :
23instantiation49, 47, 31  ⊢  
  : , : , :
24instantiation49, 33, 32  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
26instantiation49, 33, 34  ⊢  
  : , : , :
27instantiation35, 44  ⊢  
  :
28axiom  ⊢  
 proveit.logic.equality.equals_transitivity
29instantiation36, 37  ⊢  
  : , : , :
30instantiation38, 44  ⊢  
  :
31instantiation49, 39, 40  ⊢  
  : , : , :
32instantiation49, 42, 41  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
34instantiation49, 42, 54  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
36axiom  ⊢  
 proveit.logic.equality.substitution
37instantiation43, 44  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.division.frac_one_denom
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation49, 45, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
42theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
43theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
44instantiation49, 47, 48  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation49, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
48instantiation52, 53, 54  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
52theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
53instantiation55, 56  ⊢  
  : , :
54theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
55theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real