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, 4	⊢
	: , : , : , :
1	reference	29	⊢
2	instantiation	5, 73, 11, 10, 6, 12, 14, 66, 15	⊢
	: , : , : , : , : , :
3	instantiation	50, 7, 8	⊢
	: , : , :
4	instantiation	57, 15	⊢
	:
5	theorem		⊢
	proveit.numbers.multiplication.disassociation
6	instantiation	17	⊢
	: , :
7	instantiation	9, 10, 11, 73, 12, 13, 14, 66, 15	⊢
	: , : , : , : , : , :
8	instantiation	58, 16	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.association
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	17	⊢
	: , :
14	instantiation	71, 69, 18	⊢
	: , : , :
15	instantiation	71, 69, 19	⊢
	: , : , :
16	instantiation	26, 20, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	instantiation	22, 53, 70, 23	⊢
	: , :
19	instantiation	24, 25	⊢
	:
20	instantiation	26, 27, 28	⊢
	: , : , :
21	instantiation	29, 30, 31, 32	⊢
	: , : , : , :
22	theorem		⊢
	proveit.numbers.division.div_real_closure
23	instantiation	33, 76	⊢
	:
24	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
25	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
26	theorem		⊢
	proveit.logic.equality.sub_right_side_into
27	instantiation	34, 45, 35, 36	⊢
	: , : , : , : , :
28	instantiation	50, 37, 38	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
30	instantiation	58, 39	⊢
	: , : , :
31	instantiation	58, 39	⊢
	: , : , :
32	instantiation	65, 45	⊢
	:
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
34	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
35	instantiation	71, 41, 40	⊢
	: , : , :
36	instantiation	71, 41, 42	⊢
	: , : , :
37	instantiation	58, 43	⊢
	: , : , :
38	instantiation	58, 44	⊢
	: , : , :
39	instantiation	60, 45	⊢
	:
40	instantiation	71, 47, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
42	instantiation	71, 47, 48	⊢
	: , : , :
43	instantiation	58, 49	⊢
	: , : , :
44	instantiation	50, 51, 52	⊢
	: , : , :
45	instantiation	71, 69, 53	⊢
	: , : , :
46	instantiation	71, 55, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
48	instantiation	71, 55, 56	⊢
	: , : , :
49	instantiation	57, 66	⊢
	:
50	axiom		⊢
	proveit.logic.equality.equals_transitivity
51	instantiation	58, 59	⊢
	: , : , :
52	instantiation	60, 66	⊢
	:
53	instantiation	71, 61, 62	⊢
	: , : , :
54	instantiation	71, 64, 63	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
56	instantiation	71, 64, 76	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
58	axiom		⊢
	proveit.logic.equality.substitution
59	instantiation	65, 66	⊢
	:
60	theorem		⊢
	proveit.numbers.division.frac_one_denom
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
62	instantiation	71, 67, 68	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
65	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
66	instantiation	71, 69, 70	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
68	instantiation	71, 72, 73	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
70	instantiation	74, 75, 76	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
74	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
75	instantiation	77, 78	⊢
	: , :
76	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
77	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real