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, 11, 12	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.disassociation
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
3	reference	49	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	13	⊢
	: , : , :
6	instantiation	14	⊢
	: , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	reference	18	⊢
9	reference	21	⊢
10	instantiation	74, 30, 15	⊢
	: , : , :
11	instantiation	16, 17, 18, 19	⊢
	: , :
12	instantiation	20, 21, 22	⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	instantiation	23, 24, 25	⊢
	: , :
16	theorem		⊢
	proveit.numbers.division.div_complex_closure
17	instantiation	74, 30, 26	⊢
	: , : , :
18	instantiation	74, 30, 27	⊢
	: , : , :
19	instantiation	28, 68	⊢
	:
20	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
21	instantiation	74, 30, 29	⊢
	: , : , :
22	instantiation	74, 30, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
24	instantiation	32, 33	⊢
	:
25	instantiation	34, 35	⊢
	:
26	instantiation	74, 47, 36	⊢
	: , : , :
27	instantiation	74, 47, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29	instantiation	74, 38, 39	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	74, 47, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
33	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
34	theorem		⊢
	proveit.numbers.negation.real_closure
35	instantiation	41, 42, 43	⊢
	: , :
36	instantiation	74, 50, 66	⊢
	: , : , :
37	instantiation	74, 50, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
40	instantiation	74, 50, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
42	instantiation	74, 47, 46	⊢
	: , : , :
43	instantiation	74, 47, 48	⊢
	: , : , :
44	instantiation	74, 72, 49	⊢
	: , : , :
45	instantiation	70, 66	⊢
	:
46	instantiation	74, 50, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	74, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	74, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
53	instantiation	56, 57, 58	⊢
	: , :
54	instantiation	59, 60, 71	⊢
	: , :
55	assumption		⊢
56	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
57	instantiation	74, 61, 62	⊢
	: , : , :
58	instantiation	70, 63	⊢
	:
59	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
60	instantiation	64, 65, 66	⊢
	: , :
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
62	instantiation	74, 67, 68	⊢
	: , : , :
63	instantiation	74, 75, 69	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
65	instantiation	70, 71	⊢
	:
66	instantiation	74, 72, 73	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
69	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
70	theorem		⊢
	proveit.numbers.negation.int_closure
71	instantiation	74, 75, 76	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
74	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
76	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos