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