logo

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, 5  ⊢  
  : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
2instantiation52, 15, 6  ⊢  
  : , : , :
3instantiation52, 15, 7  ⊢  
  : , : , :
4instantiation8, 9, 10  ⊢  
  :
5instantiation52, 11, 12  ⊢  
  : , : , :
6instantiation52, 23, 13  ⊢  
  : , : , :
7instantiation52, 23, 14  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
9instantiation52, 15, 16  ⊢  
  : , : , :
10instantiation17, 18, 19  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
12instantiation52, 20, 21  ⊢  
  : , : , :
13instantiation52, 32, 48  ⊢  
  : , : , :
14instantiation52, 32, 22  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
16instantiation52, 23, 24  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
18instantiation52, 27, 25  ⊢  
  : , : , :
19instantiation52, 27, 26  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
21instantiation52, 27, 28  ⊢  
  : , : , :
22instantiation29, 30, 31  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
24instantiation52, 32, 42  ⊢  
  : , : , :
25instantiation52, 34, 33  ⊢  
  : , : , :
26instantiation52, 34, 51  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
28instantiation52, 34, 35  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
30instantiation36, 37  ⊢  
  : , :
31theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_in_m_domain
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
33theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
34theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
35theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
36theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
37instantiation38, 39, 40  ⊢  
  : , :
38theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
39theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
40instantiation41, 42, 43  ⊢  
  : , :
41theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
42instantiation44, 45, 46  ⊢  
  : , :
43instantiation47, 48  ⊢  
  :
44theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
45instantiation52, 53, 49  ⊢  
  : , : , :
46instantiation52, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.negation.int_closure
48instantiation52, 53, 54  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
50theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
51axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1