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.neg_frac_neg_numerator
2	reference	7	⊢
3	reference	8	⊢
4	reference	9	⊢
5	instantiation	6, 7, 8, 9, 10^*	⊢
	: , :
6	theorem		⊢
	proveit.numbers.division.div_as_mult
7	instantiation	86, 61, 11	⊢
	: , : , :
8	instantiation	86, 61, 12	⊢
	: , : , :
9	instantiation	27, 16	⊢
	:
10	instantiation	38, 13, 14	⊢
	: , : , :
11	instantiation	77, 78, 15	⊢
	: , : , :
12	instantiation	77, 78, 16	⊢
	: , : , :
13	instantiation	31, 17	⊢
	: , : , :
14	instantiation	18, 44, 19, 60, 22, 20^*	⊢
	: , : , :
15	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
16	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
17	instantiation	21, 44, 70, 62, 22, 23^*	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
19	instantiation	24, 70, 62	⊢
	: , :
20	instantiation	38, 25, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
22	instantiation	27, 74	⊢
	:
23	instantiation	28, 52, 29, 30^*	⊢
	: , :
24	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
25	instantiation	31, 32	⊢
	: , : , :
26	instantiation	33, 34, 90, 35^*	⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
29	instantiation	86, 61, 36	⊢
	: , : , :
30	instantiation	37, 52	⊢
	:
31	axiom		⊢
	proveit.logic.equality.substitution
32	instantiation	38, 39, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
34	instantiation	86, 41, 42	⊢
	: , : , :
35	instantiation	43, 44	⊢
	:
36	instantiation	86, 66, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	46, 47, 83, 68, 48, 49, 52, 53, 50	⊢
	: , : , : , : , : , :
40	instantiation	51, 52, 53, 54	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
42	instantiation	86, 55, 56	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
44	instantiation	86, 61, 57	⊢
	: , : , :
45	instantiation	86, 75, 58	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.disassociation
47	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
48	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49	instantiation	59	⊢
	: , :
50	instantiation	86, 61, 60	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
52	instantiation	86, 61, 70	⊢
	: , : , :
53	instantiation	86, 61, 62	⊢
	: , : , :
54	instantiation	63	⊢
	:
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
56	instantiation	86, 64, 65	⊢
	: , : , :
57	instantiation	86, 66, 67	⊢
	: , : , :
58	instantiation	86, 82, 68	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
60	instantiation	69, 70	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
62	instantiation	86, 71, 72	⊢
	: , : , :
63	axiom		⊢
	proveit.logic.equality.equals_reflexivity
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
65	instantiation	86, 73, 74	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	86, 75, 76	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.numbers.negation.real_closure
70	instantiation	77, 78, 79	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
72	instantiation	86, 80, 81	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
74	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
76	instantiation	86, 82, 83	⊢
	: , : , :
77	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
78	instantiation	84, 85	⊢
	: , :
79	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
81	instantiation	86, 87, 88	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
84	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
88	instantiation	89, 90	⊢
	:
89	theorem		⊢
	proveit.numbers.negation.int_neg_closure
90	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
^*equality replacement requirements