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.statistics.prob_of_all_events_transformation
2	theorem		⊢
	proveit.physics.quantum.QPE._Omega_is_sample_space
3	instantiation	7, 8	⊢
	: , :
4	instantiation	9, 29, 60, 65, 56	⊢
	: , : , : , : , :
5	instantiation	10, 11	⊢
	: , : , :
6	instantiation	12, 31, 67, 32, 13, 43, 14, 15^*	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
8	instantiation	16, 17	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.modular.interval_left_shift_bijection
10	axiom		⊢
	proveit.logic.equality.substitution
11	instantiation	18, 19	⊢
	: , :
12	theorem		⊢
	proveit.numbers.modular.redundant_mod_elimination_in_sum_in_modabs
13	instantiation	68, 52, 20	⊢
	: , : , :
14	instantiation	68, 21, 22	⊢
	: , : , :
15	instantiation	23, 24, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.sets.functions.bijections.membership_unfolding
17	theorem		⊢
	proveit.physics.quantum.QPE._sample_space_bijection
18	theorem		⊢
	proveit.logic.equality.equals_reversal
19	instantiation	26, 56, 54	⊢
	: , :
20	instantiation	68, 55, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
22	instantiation	68, 28, 29	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	30, 31, 40, 67, 32, 33, 36, 37, 34	⊢
	: , : , : , : , : , :
25	instantiation	35, 36, 37, 38	⊢
	: , : , :
26	axiom		⊢
	proveit.physics.quantum.QPE._mod_add_def
27	instantiation	61, 56, 54	⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
29	instantiation	39, 40, 41	⊢
	: , :
30	theorem		⊢
	proveit.numbers.addition.disassociation
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	42	⊢
	: , :
34	instantiation	68, 44, 43	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
36	instantiation	68, 44, 50	⊢
	: , : , :
37	instantiation	68, 44, 45	⊢
	: , : , :
38	instantiation	46	⊢
	:
39	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	instantiation	68, 47, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	instantiation	49, 50	⊢
	:
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	68, 52, 51	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.equals_reflexivity
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
48	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
49	theorem		⊢
	proveit.numbers.negation.real_closure
50	instantiation	68, 52, 53	⊢
	: , : , :
51	instantiation	68, 55, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	68, 55, 56	⊢
	: , : , :
54	instantiation	68, 57, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
57	instantiation	59, 60, 65	⊢
	: , :
58	assumption		⊢
59	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
60	instantiation	61, 62, 63	⊢
	: , :
61	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
62	instantiation	64, 65	⊢
	:
63	instantiation	68, 66, 67	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	68, 69, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
70	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements