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	, ⊢
	: , :
1	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
3	instantiation	7	⊢
	: , : , :
4	instantiation	99, 16, 8	⊢
	: , : , :
5	instantiation	99, 16, 9	⊢
	: , : , :
6	instantiation	10, 11, 12	, ⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
8	instantiation	99, 14, 13	⊢
	: , : , :
9	instantiation	99, 14, 15	⊢
	: , : , :
10	theorem		⊢
	proveit.logic.equality.sub_right_side_into
11	instantiation	99, 16, 17	, ⊢
	: , : , :
12	instantiation	28, 18	⊢
	: , : , :
13	instantiation	99, 20, 19	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
15	instantiation	99, 20, 21	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
17	instantiation	99, 22, 23	, ⊢
	: , : , :
18	instantiation	28, 24	⊢
	: , : , :
19	instantiation	99, 25, 81	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
21	instantiation	99, 25, 54	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
23	instantiation	26, 27	, ⊢
	:
24	instantiation	28, 29	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
26	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
27	instantiation	30, 31, 32	, ⊢
	:
28	axiom		⊢
	proveit.logic.equality.substitution
29	instantiation	33, 34, 35, 36, 37^*	⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
31	instantiation	99, 75, 38	⊢
	: , : , :
32	instantiation	39, 40	, ⊢
	: , :
33	theorem		⊢
	proveit.numbers.division.div_as_mult
34	instantiation	99, 75, 41	⊢
	: , : , :
35	instantiation	99, 75, 42	⊢
	: , : , :
36	instantiation	80, 54	⊢
	:
37	instantiation	43, 44, 76, 45, 72, 46^*	⊢
	: , : , :
38	instantiation	47, 48, 60, 49	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
40	instantiation	50, 51, 65, 52	, ⊢
	: , :
41	instantiation	99, 78, 53	⊢
	: , : , :
42	instantiation	84, 85, 54	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
44	instantiation	99, 75, 71	⊢
	: , : , :
45	instantiation	99, 78, 55	⊢
	: , : , :
46	instantiation	56, 68, 57, 58^*	⊢
	: , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
48	instantiation	59, 60	⊢
	:
49	instantiation	61, 74	⊢
	:
50	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
51	instantiation	62, 63, 98, 64	⊢
	: , : , : , : , :
52	assumption		⊢
53	instantiation	99, 87, 65	⊢
	: , : , :
54	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
55	instantiation	99, 87, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
57	instantiation	99, 75, 70	⊢
	: , : , :
58	instantiation	67, 68	⊢
	:
59	theorem		⊢
	proveit.numbers.negation.real_closure
60	instantiation	69, 70, 71, 72	⊢
	: , :
61	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
62	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
63	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
64	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
65	instantiation	99, 73, 74	⊢
	: , : , :
66	instantiation	95, 91	⊢
	:
67	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
68	instantiation	99, 75, 76	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.division.div_real_closure
70	instantiation	99, 78, 77	⊢
	: , : , :
71	instantiation	99, 78, 79	⊢
	: , : , :
72	instantiation	80, 81	⊢
	:
73	instantiation	82, 83, 96	⊢
	: , :
74	assumption		⊢
75	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
76	instantiation	84, 85, 86	⊢
	: , : , :
77	instantiation	99, 87, 91	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	99, 87, 88	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
81	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
82	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
83	instantiation	89, 90, 91	⊢
	: , :
84	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
85	instantiation	92, 93	⊢
	: , :
86	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
88	instantiation	99, 97, 94	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
90	instantiation	95, 96	⊢
	:
91	instantiation	99, 97, 98	⊢
	: , : , :
92	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
94	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
95	theorem		⊢
	proveit.numbers.negation.int_closure
96	instantiation	99, 100, 101	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
99	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
101	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements