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