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	25	⊢
2	instantiation	25, 4, 5	⊢
	: , : , :
3	instantiation	25, 6, 7	⊢
	: , : , :
4	instantiation	58, 8	⊢
	: , : , :
5	instantiation	9, 76, 10, 11, 68, 12, 13, 14^*	⊢
	: , : , : , : , : , :
6	axiom		⊢
	proveit.physics.quantum.QPE._best_round_def
7	instantiation	15, 16	⊢
	:
8	instantiation	17, 71	⊢
	:
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	74, 72, 23	⊢
	: , : , :
13	instantiation	18, 45, 68, 19	⊢
	: , :
14	instantiation	25, 20, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.rounding.round_in_terms_of_floor
16	instantiation	22, 73, 23	⊢
	: , :
17	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
18	theorem		⊢
	proveit.numbers.division.div_complex_closure
19	instantiation	24, 79	⊢
	:
20	instantiation	25, 26, 27	⊢
	: , : , :
21	instantiation	28, 29, 30, 31	⊢
	: , : , : , :
22	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
23	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
25	theorem		⊢
	proveit.logic.equality.sub_right_side_into
26	instantiation	32, 44, 45, 33, 34	⊢
	: , : , : , : , :
27	instantiation	49, 35, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
29	instantiation	58, 37	⊢
	: , : , :
30	instantiation	58, 38	⊢
	: , : , :
31	instantiation	67, 45	⊢
	:
32	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
33	instantiation	74, 40, 39	⊢
	: , : , :
34	instantiation	74, 40, 41	⊢
	: , : , :
35	instantiation	58, 42	⊢
	: , : , :
36	instantiation	58, 43	⊢
	: , : , :
37	instantiation	60, 44	⊢
	:
38	instantiation	60, 45	⊢
	:
39	instantiation	74, 47, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
41	instantiation	74, 47, 48	⊢
	: , : , :
42	instantiation	49, 50, 51	⊢
	: , : , :
43	instantiation	58, 52	⊢
	: , : , :
44	instantiation	74, 72, 53	⊢
	: , : , :
45	instantiation	74, 72, 54	⊢
	: , : , :
46	instantiation	74, 56, 55	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
48	instantiation	74, 56, 57	⊢
	: , : , :
49	axiom		⊢
	proveit.logic.equality.equals_transitivity
50	instantiation	58, 59	⊢
	: , : , :
51	instantiation	60, 68	⊢
	:
52	instantiation	61, 68	⊢
	:
53	instantiation	74, 63, 62	⊢
	: , : , :
54	instantiation	74, 63, 64	⊢
	: , : , :
55	instantiation	74, 65, 79	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	74, 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	74, 70, 69	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
64	instantiation	74, 70, 71	⊢
	: , : , :
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	74, 72, 73	⊢
	: , : , :
69	instantiation	74, 75, 76	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
71	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
72	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
73	instantiation	77, 78, 79	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
77	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
78	instantiation	80, 81	⊢
	: , :
79	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
80	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
^*equality replacement requirements