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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_right_side_into
2instantiation4, 5, 6, 7, 8, 9  ⊢  
  : , : , : , : , :
3instantiation19, 10  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
5instantiation59, 60, 11  ⊢  
  : , : , :
6instantiation12, 13, 14  ⊢  
  : , :
7instantiation59, 17, 15  ⊢  
  : , : , :
8instantiation59, 17, 16  ⊢  
  : , : , :
9instantiation59, 17, 18  ⊢  
  : , : , :
10instantiation19, 20  ⊢  
  : , : , :
11instantiation59, 32, 21  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
13instantiation59, 60, 22  ⊢  
  : , : , :
14instantiation59, 60, 23  ⊢  
  : , : , :
15instantiation59, 25, 24  ⊢  
  : , : , :
16instantiation59, 25, 26  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
18instantiation59, 27, 28  ⊢  
  : , : , :
19axiom  ⊢  
 proveit.logic.equality.substitution
20instantiation29, 30  ⊢  
  :
21instantiation59, 43, 31  ⊢  
  : , : , :
22instantiation59, 32, 33  ⊢  
  : , : , :
23instantiation59, 34, 40  ⊢  
  : , : , :
24instantiation59, 36, 35  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
26instantiation59, 36, 37  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
28instantiation38, 39, 40  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
30instantiation59, 60, 41  ⊢  
  : , : , :
31instantiation59, 52, 42  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
33instantiation59, 43, 44  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
35instantiation59, 46, 45  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37instantiation59, 46, 51  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.multiplication.mult_real_pos_closure_bin
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
40instantiation47, 48  ⊢  
  :
41instantiation49, 50, 51  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation59, 52, 53  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
46theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
47theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
48instantiation54, 55, 56  ⊢  
  :
49theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
50instantiation57, 58  ⊢  
  : , :
51theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
55instantiation59, 60, 61  ⊢  
  : , : , :
56assumption  ⊢  
57theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
59theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
61instantiation62, 63  ⊢  
  :
62theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
63theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int