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