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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
10instantiation72, 18, 17  ⊢  
  : , : , :
11instantiation72, 18, 19  ⊢  
  : , : , :
12instantiation20, 21, 22  ⊢  
  : , : , :
13instantiation23, 28  ⊢  
  :
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation24, 34, 71, 35, 36, 37, 38, 39, 28, 40  ⊢  
  : , : , : , : , : , : , :
16instantiation25, 35, 26, 34, 27, 36, 28, 38, 39, 40  ⊢  
  : , : , : , : , : , :
17instantiation72, 29, 48  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19instantiation72, 30, 31  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
21instantiation72, 73, 32  ⊢  
  : , : , :
22instantiation33, 34, 71, 35, 36, 37, 38, 39, 40  ⊢  
  : , : , : , : , : , :
23theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
24theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
25theorem  ⊢  
 proveit.numbers.multiplication.association
26theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
27instantiation41  ⊢  
  : , : , :
28instantiation72, 73, 42  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31instantiation72, 43, 44  ⊢  
  : , : , :
32instantiation51, 45, 47  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.multiplication.disassociation
34axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
35theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
36theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37instantiation46  ⊢  
  : , :
38instantiation72, 73, 52  ⊢  
  : , : , :
39instantiation72, 73, 53  ⊢  
  : , : , :
40instantiation72, 73, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
42instantiation72, 54, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
44instantiation72, 49, 50  ⊢  
  : , : , :
45instantiation51, 52, 53  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47instantiation72, 54, 55  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
50theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
51theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
52instantiation72, 56, 57  ⊢  
  : , : , :
53instantiation58, 59, 60  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
55instantiation61, 62  ⊢  
  :
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
57instantiation72, 63, 64  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
59instantiation65, 66  ⊢  
  : , :
60theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
61theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
62instantiation67, 68, 69  ⊢  
  :
63theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
64instantiation72, 70, 71  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
66theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
67theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
68instantiation72, 73, 74  ⊢  
  : , : , :
69assumption  ⊢  
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
71theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
72theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
73theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
74instantiation75, 76  ⊢  
  :
75theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
76theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int
*equality replacement requirements