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 type	requirements	statement
0	instantiation	1, 2, 3	⊢
	: , : , :
1	reference	21	⊢
2	instantiation	21, 4, 5	⊢
	: , : , :
3	instantiation	21, 6, 7	⊢
	: , : , :
4	instantiation	58, 8	⊢
	: , : , :
5	instantiation	9, 96, 10, 11, 68, 15, 12, 13^*	⊢
	: , : , : , : , : , :
6	axiom		⊢
	proveit.physics.quantum.QPE._best_floor_def
7	instantiation	14, 68, 15	⊢
	: , :
8	instantiation	16, 69	⊢
	:
9	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	17, 42, 68, 36	⊢
	: , :
13	instantiation	21, 18, 19	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.commutation
15	instantiation	94, 70, 20	⊢
	: , : , :
16	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
17	theorem		⊢
	proveit.numbers.division.div_complex_closure
18	instantiation	21, 22, 23	⊢
	: , : , :
19	instantiation	24, 25, 26, 27	⊢
	: , : , : , :
20	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	28, 41, 42, 29, 30	⊢
	: , : , : , : , :
23	instantiation	48, 31, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
25	instantiation	58, 33	⊢
	: , : , :
26	instantiation	58, 34	⊢
	: , : , :
27	instantiation	67, 42	⊢
	:
28	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
29	instantiation	35, 68, 36	⊢
	:
30	instantiation	94, 37, 38	⊢
	: , : , :
31	instantiation	58, 39	⊢
	: , : , :
32	instantiation	58, 40	⊢
	: , : , :
33	instantiation	60, 41	⊢
	:
34	instantiation	60, 42	⊢
	:
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
36	instantiation	43, 44, 45	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
38	instantiation	94, 46, 47	⊢
	: , : , :
39	instantiation	48, 49, 50	⊢
	: , : , :
40	instantiation	58, 51	⊢
	: , : , :
41	instantiation	94, 70, 52	⊢
	: , : , :
42	instantiation	94, 70, 53	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
44	instantiation	94, 56, 54	⊢
	: , : , :
45	instantiation	94, 56, 55	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
47	instantiation	94, 56, 57	⊢
	: , : , :
48	axiom		⊢
	proveit.logic.equality.equals_transitivity
49	instantiation	58, 59	⊢
	: , : , :
50	instantiation	60, 68	⊢
	:
51	instantiation	61, 68	⊢
	:
52	instantiation	94, 75, 62	⊢
	: , : , :
53	instantiation	94, 75, 63	⊢
	: , : , :
54	instantiation	94, 65, 64	⊢
	: , : , :
55	instantiation	94, 65, 93	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	94, 65, 66	⊢
	: , : , :
58	axiom		⊢
	proveit.logic.equality.substitution
59	instantiation	67, 68	⊢
	:
60	theorem		⊢
	proveit.numbers.division.frac_one_denom
61	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
62	instantiation	94, 79, 90	⊢
	: , : , :
63	instantiation	94, 79, 69	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
67	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
68	instantiation	94, 70, 71	⊢
	: , : , :
69	instantiation	72, 73, 74	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
71	instantiation	94, 75, 76	⊢
	: , : , :
72	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
73	instantiation	77, 78	⊢
	: , :
74	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_in_m_domain
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	94, 79, 84	⊢
	: , : , :
77	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
78	instantiation	80, 81, 82	⊢
	: , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
80	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
81	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
82	instantiation	83, 84, 85	⊢
	: , :
83	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
84	instantiation	86, 87, 88	⊢
	: , :
85	instantiation	89, 90	⊢
	:
86	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
87	instantiation	94, 95, 91	⊢
	: , : , :
88	instantiation	94, 92, 93	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.negation.int_closure
90	instantiation	94, 95, 96	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
92	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
93	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
94	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
95	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
96	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements