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, 5, 6, 7, 8, 9, 10	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.disassociation
2	reference	78	⊢
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	11	⊢
	: , : , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	79, 47, 12	⊢
	: , : , :
8	instantiation	13, 14, 15, 16	⊢
	: , :
9	instantiation	79, 47, 51	⊢
	: , : , :
10	instantiation	17, 18, 19	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
12	instantiation	79, 53, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.division.div_complex_closure
14	instantiation	79, 47, 21	⊢
	: , : , :
15	instantiation	79, 47, 22	⊢
	: , : , :
16	instantiation	23, 24	⊢
	:
17	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
18	instantiation	79, 47, 25	⊢
	: , : , :
19	instantiation	79, 47, 26	⊢
	: , : , :
20	instantiation	79, 55, 27	⊢
	: , : , :
21	instantiation	79, 53, 28	⊢
	: , : , :
22	instantiation	79, 53, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
25	instantiation	79, 30, 31	⊢
	: , : , :
26	instantiation	79, 53, 32	⊢
	: , : , :
27	instantiation	79, 77, 33	⊢
	: , : , :
28	instantiation	79, 55, 71	⊢
	: , : , :
29	instantiation	79, 55, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
31	instantiation	35, 36	⊢
	:
32	instantiation	79, 55, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
34	instantiation	79, 77, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
36	instantiation	39, 40, 41	⊢
	: , :
37	instantiation	75, 71	⊢
	:
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
39	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
40	instantiation	79, 47, 42	⊢
	: , : , :
41	instantiation	43, 44	⊢
	:
42	instantiation	45, 46	⊢
	:
43	theorem		⊢
	proveit.numbers.negation.complex_closure
44	instantiation	79, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
46	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	49, 50, 51	⊢
	: , :
49	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
50	instantiation	79, 53, 52	⊢
	: , : , :
51	instantiation	79, 53, 54	⊢
	: , : , :
52	instantiation	79, 55, 56	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	79, 57, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	79, 59, 60	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
58	instantiation	61, 62, 63	⊢
	: , :
59	instantiation	64, 65, 76	⊢
	: , :
60	assumption		⊢
61	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
62	instantiation	79, 66, 67	⊢
	: , : , :
63	instantiation	75, 68	⊢
	:
64	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
65	instantiation	69, 70, 71	⊢
	: , :
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
67	instantiation	79, 72, 73	⊢
	: , : , :
68	instantiation	79, 80, 74	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
70	instantiation	75, 76	⊢
	:
71	instantiation	79, 77, 78	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
74	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
75	theorem		⊢
	proveit.numbers.negation.int_closure
76	instantiation	79, 80, 81	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
79	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
81	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos