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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  ⊢  
  : , : , :
1reference14  ⊢  
2instantiation14, 4, 5  ⊢  
  : , : , :
3instantiation6, 12  ⊢  
  :
4instantiation7, 8  ⊢  
  : , : , :
5instantiation9, 10, 11, 12, 13*  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.division.frac_one_denom
7axiom  ⊢  
 proveit.logic.equality.substitution
8instantiation14, 15, 16  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
10instantiation75, 18, 17  ⊢  
  : , : , :
11instantiation75, 18, 19  ⊢  
  : , : , :
12instantiation20, 21, 22  ⊢  
  : , : , :
13instantiation23, 29  ⊢  
  :
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation24, 35, 36, 69, 37, 25, 39, 29, 40, 41  ⊢  
  : , : , : , : , : , : , :
16instantiation26, 36, 27, 35, 28, 37, 29, 39, 40, 41  ⊢  
  : , : , : , : , : , :
17instantiation75, 31, 30  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19instantiation75, 31, 32  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
21instantiation75, 76, 33  ⊢  
  : , : , :
22instantiation34, 35, 69, 36, 37, 38, 39, 40, 41  ⊢  
  : , : , : , : , : , :
23theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
24theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
25instantiation48  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.multiplication.association
27theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
28instantiation42  ⊢  
  : , : , :
29instantiation75, 76, 43  ⊢  
  : , : , :
30instantiation75, 45, 44  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
32instantiation75, 45, 46  ⊢  
  : , : , :
33instantiation55, 47, 49  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.multiplication.disassociation
35axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
36theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
37theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38instantiation48  ⊢  
  : , :
39instantiation75, 76, 56  ⊢  
  : , : , :
40instantiation75, 76, 57  ⊢  
  : , : , :
41instantiation75, 76, 49  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
43instantiation75, 50, 51  ⊢  
  : , : , :
44instantiation75, 53, 52  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
46instantiation75, 53, 54  ⊢  
  : , : , :
47instantiation55, 56, 57  ⊢  
  : , :
48theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
49instantiation75, 64, 58  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation75, 59, 60  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
55theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
56instantiation61, 62, 63  ⊢  
  : , : , :
57instantiation75, 64, 65  ⊢  
  : , : , :
58instantiation66, 67  ⊢  
  :
59theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
60instantiation75, 68, 69  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
62instantiation70, 71  ⊢  
  : , :
63theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
64theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
65theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
66theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
67instantiation72, 73, 74  ⊢  
  :
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
69theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
70theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
71theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
72theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
73instantiation75, 76, 77  ⊢  
  : , : , :
74assumption  ⊢  
75theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
77instantiation78, 79  ⊢  
  :
78theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
79theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int
*equality replacement requirements