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	generalization	1	⊢
1	instantiation	2, 3	, ⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.equals_reversal
3	instantiation	4, 14, 5, 6, 7^*	, ⊢
	: , : , : , :
4	theorem		⊢
	proveit.numbers.division.prod_of_fracs
5	instantiation	99, 8, 9	⊢
	: , : , :
6	instantiation	10, 11, 12	, ⊢
	: , :
7	instantiation	13, 14	⊢
	:
8	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
9	instantiation	99, 15, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
11	instantiation	17, 18, 19	, ⊢
	:
12	instantiation	99, 24, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
14	instantiation	99, 24, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
16	instantiation	99, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
18	instantiation	99, 24, 25	, ⊢
	: , : , :
19	instantiation	26, 27	, ⊢
	: , :
20	instantiation	99, 37, 28	⊢
	: , : , :
21	instantiation	99, 37, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
23	instantiation	99, 30, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
25	instantiation	32, 33, 34	, ⊢
	: , :
26	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
27	instantiation	35, 36	, ⊢
	: , :
28	instantiation	99, 44, 98	⊢
	: , : , :
29	instantiation	99, 44, 88	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
32	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
33	instantiation	99, 37, 38	, ⊢
	: , : , :
34	instantiation	39, 40	⊢
	:
35	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
36	instantiation	41, 42, 52, 43	, ⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	99, 44, 52	, ⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.negation.real_closure
40	instantiation	45, 46, 47	⊢
	: , :
41	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
42	instantiation	48, 49, 91, 50	⊢
	: , : , : , : , :
43	instantiation	51, 52, 53, 54	, ⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
45	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
46	instantiation	55, 56, 57	⊢
	: , : , :
47	instantiation	58, 59	⊢
	:
48	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
49	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
50	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
51	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
52	instantiation	99, 60, 69	, ⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
54	instantiation	61, 62, 63	, ⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
56	instantiation	64, 65	⊢
	: , :
57	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
58	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
59	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
60	instantiation	86, 67, 68	⊢
	: , :
61	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
62	instantiation	66, 67, 68, 69	, ⊢
	: , : , :
63	instantiation	70, 71	⊢
	:
64	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
66	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
67	instantiation	92, 72, 88	⊢
	: , :
68	instantiation	97, 73	⊢
	:
69	assumption		⊢
70	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
71	instantiation	74, 75	⊢
	:
72	instantiation	97, 93	⊢
	:
73	instantiation	92, 80, 88	⊢
	: , :
74	theorem		⊢
	proveit.numbers.negation.int_neg_closure
75	instantiation	76, 77, 78	⊢
	: , :
76	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
77	instantiation	79, 80, 81	⊢
	:
78	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
79	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
80	instantiation	99, 82, 90	⊢
	: , : , :
81	instantiation	83, 84, 85	⊢
	: , : , :
82	instantiation	86, 88, 89	⊢
	: , :
83	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
84	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
85	instantiation	87, 88, 89, 90	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
87	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
88	instantiation	99, 100, 91	⊢
	: , : , :
89	instantiation	92, 93, 94	⊢
	: , :
90	assumption		⊢
91	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
92	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
93	instantiation	99, 95, 96	⊢
	: , : , :
94	instantiation	97, 98	⊢
	:
95	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
96	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
97	theorem		⊢
	proveit.numbers.negation.int_closure
98	instantiation	99, 100, 101	⊢
	: , : , :
99	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements