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	theorem		⊢
	proveit.numbers.division.div_real_closure
2	instantiation	97, 42, 5	⊢
	: , : , :
3	instantiation	50, 6, 7	, ⊢
	: , :
4	instantiation	8, 99, 9, 10, 11	, ⊢
	: , :
5	instantiation	97, 49, 86	⊢
	: , : , :
6	instantiation	97, 42, 12	⊢
	: , : , :
7	instantiation	13, 31, 99	, ⊢
	: , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
9	instantiation	14	⊢
	: , :
10	instantiation	97, 15, 16	⊢
	: , : , :
11	instantiation	17, 18, 19	, ⊢
	: , :
12	instantiation	97, 49, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
16	instantiation	97, 21, 22	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
18	instantiation	23, 24, 25	, ⊢
	:
19	instantiation	97, 30, 26	⊢
	: , : , :
20	instantiation	97, 98, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
22	instantiation	97, 28, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
24	instantiation	97, 30, 31	, ⊢
	: , : , :
25	instantiation	32, 33	, ⊢
	: , :
26	instantiation	97, 42, 34	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
28	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
29	instantiation	97, 35, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	37, 38, 39	, ⊢
	: , :
32	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
33	instantiation	40, 41	, ⊢
	: , :
34	instantiation	97, 49, 96	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
37	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
38	instantiation	97, 42, 43	, ⊢
	: , : , :
39	instantiation	44, 45	⊢
	:
40	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
41	instantiation	46, 47, 63, 48	, ⊢
	: , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	97, 49, 63	, ⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.negation.real_closure
45	instantiation	50, 51, 52	⊢
	: , :
46	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
47	instantiation	53, 54, 89, 55	⊢
	: , : , : , : , :
48	instantiation	56, 57	, ⊢
	:
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
51	instantiation	58, 59, 60	⊢
	: , : , :
52	instantiation	61, 62	⊢
	:
53	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
54	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
55	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
56	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
57	instantiation	77, 63, 64	, ⊢
	:
58	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
59	instantiation	65, 66	⊢
	: , :
60	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
61	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
62	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
63	instantiation	97, 67, 73	, ⊢
	: , : , :
64	instantiation	81, 68, 69	, ⊢
	: , : , :
65	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
67	instantiation	84, 72, 91	⊢
	: , :
68	instantiation	70, 71	⊢
	:
69	instantiation	85, 72, 91, 73	, ⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
71	instantiation	74, 75, 76	⊢
	: , :
72	instantiation	90, 78, 86	⊢
	: , :
73	assumption		⊢
74	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
75	instantiation	77, 78, 79	⊢
	:
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
77	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
78	instantiation	97, 80, 88	⊢
	: , : , :
79	instantiation	81, 82, 83	⊢
	: , : , :
80	instantiation	84, 86, 87	⊢
	: , :
81	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
82	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
83	instantiation	85, 86, 87, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
85	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
86	instantiation	97, 98, 89	⊢
	: , : , :
87	instantiation	90, 91, 92	⊢
	: , :
88	assumption		⊢
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
90	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
91	instantiation	97, 93, 94	⊢
	: , : , :
92	instantiation	95, 96	⊢
	:
93	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
94	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
95	theorem		⊢
	proveit.numbers.negation.int_closure
96	instantiation	97, 98, 99	⊢
	: , : , :
97	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
98	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat2