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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*  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
2instantiation58, 7, 6  ⊢  
  : , : , :
3instantiation58, 7, 8  ⊢  
  : , : , :
4instantiation9, 10, 11  ⊢  
  : , : , :
5instantiation12, 13  ⊢  
  :
6instantiation58, 15, 14  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
8instantiation58, 15, 16  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
10instantiation58, 59, 17  ⊢  
  : , : , :
11instantiation18, 19, 52, 20, 21, 22, 23, 24, 25  ⊢  
  : , : , : , : , : , :
12theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
13instantiation58, 59, 26  ⊢  
  : , : , :
14instantiation58, 28, 27  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
16instantiation58, 28, 29  ⊢  
  : , : , :
17instantiation38, 30, 32  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.multiplication.disassociation
19axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
20theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
21theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22instantiation31  ⊢  
  : , :
23instantiation58, 59, 39  ⊢  
  : , : , :
24instantiation58, 59, 40  ⊢  
  : , : , :
25instantiation58, 59, 32  ⊢  
  : , : , :
26instantiation58, 33, 34  ⊢  
  : , : , :
27instantiation58, 36, 35  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
29instantiation58, 36, 37  ⊢  
  : , : , :
30instantiation38, 39, 40  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32instantiation58, 47, 41  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
34instantiation58, 42, 43  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
36theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
37theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
38theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
39instantiation44, 45, 46  ⊢  
  : , : , :
40instantiation58, 47, 48  ⊢  
  : , : , :
41instantiation49, 50  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
43instantiation58, 51, 52  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
45instantiation53, 54  ⊢  
  : , :
46theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
50instantiation55, 56, 57  ⊢  
  :
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
53theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
55theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
56instantiation58, 59, 60  ⊢  
  : , : , :
57assumption  ⊢  
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
60instantiation61, 62  ⊢  
  :
61theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
62theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int
*equality replacement requirements