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	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
4	reference	73	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	11	⊢
	: , : , :
7	reference	21	⊢
8	reference	24	⊢
9	instantiation	74, 34, 12	⊢
	: , : , :
10	instantiation	13, 14, 15	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
12	instantiation	16, 17, 18	⊢
	: , :
13	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
14	instantiation	19, 20, 21, 22	⊢
	: , :
15	instantiation	23, 24, 25	⊢
	: , :
16	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
17	instantiation	26, 27	⊢
	:
18	instantiation	28, 29	⊢
	:
19	theorem		⊢
	proveit.numbers.division.div_complex_closure
20	instantiation	74, 34, 30	⊢
	: , : , :
21	instantiation	74, 34, 31	⊢
	: , : , :
22	instantiation	32, 68	⊢
	:
23	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
24	instantiation	74, 34, 33	⊢
	: , : , :
25	instantiation	74, 34, 35	⊢
	: , : , :
26	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
27	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
28	theorem		⊢
	proveit.numbers.negation.real_closure
29	instantiation	36, 37, 38	⊢
	: , :
30	instantiation	74, 45, 39	⊢
	: , : , :
31	instantiation	74, 45, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
33	instantiation	74, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	74, 45, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
37	instantiation	74, 45, 44	⊢
	: , : , :
38	instantiation	74, 45, 46	⊢
	: , : , :
39	instantiation	74, 49, 66	⊢
	: , : , :
40	instantiation	74, 49, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
43	instantiation	74, 49, 48	⊢
	: , : , :
44	instantiation	74, 49, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	74, 51, 52	⊢
	: , : , :
47	instantiation	74, 72, 53	⊢
	: , : , :
48	instantiation	70, 66	⊢
	:
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	74, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
52	instantiation	56, 57, 58	⊢
	: , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
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