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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, 4, 5, 6, 7*, ,  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.division.div_neq_real
2reference33  ⊢  
3instantiation8, 33, 28  ⊢  
  : , :
4instantiation52, 39, 9  ⊢  
  : , : , :
5instantiation10, 42, 16, 11, ,  ⊢  
  : , :
6instantiation12, 54  ⊢  
  :
7instantiation13, 14, 15  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
9instantiation52, 45, 16  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
11assumption  ⊢  
12theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
13axiom  ⊢  
 proveit.logic.equality.equals_transitivity
14instantiation17, 18, 19, 22, 20*  ⊢  
  : , : , :
15instantiation21, 22  ⊢  
  :
16assumption  ⊢  
17theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
18instantiation52, 24, 23  ⊢  
  : , : , :
19instantiation52, 24, 25  ⊢  
  : , : , :
20instantiation26, 27  ⊢  
  :
21theorem  ⊢  
 proveit.numbers.division.frac_one_denom
22instantiation52, 32, 28  ⊢  
  : , : , :
23instantiation52, 30, 29  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
25instantiation52, 30, 31  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
27instantiation52, 32, 33  ⊢  
  : , : , :
28instantiation34, 35  ⊢  
  :
29instantiation52, 37, 36  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31instantiation52, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation52, 39, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
35instantiation41, 42  ⊢  
  :
36instantiation52, 43, 54  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38instantiation52, 43, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation52, 45, 46  ⊢  
  : , : , :
41instantiation47, 48, 49, 50, 51  ⊢  
  : , : , : , :
42assumption  ⊢  
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation52, 53, 54  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.enumeration.true_for_each_then_true_for_all
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
49instantiation55  ⊢  
  : , :
50theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
51theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
54theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
55theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
*equality replacement requirements