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	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	4, 5	⊢
	:
3	instantiation	6, 7, 8, 9, 10^, 11^	⊢
	: , : , : , : , : , : , : , :
4	axiom		⊢
	proveit.physics.quantum.QPE._fail_def
5	assumption		⊢
6	theorem		⊢
	proveit.statistics.prob_of_all_events_transformation
7	theorem		⊢
	proveit.physics.quantum.QPE._Omega_is_sample_space
8	instantiation	12, 13	⊢
	: , :
9	instantiation	14, 34, 65, 70, 61	⊢
	: , : , : , : , :
10	instantiation	15, 16	⊢
	: , : , :
11	instantiation	17, 36, 72, 37, 18, 48, 19, 20^*	⊢
	: , : , : , : , : , :
12	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
13	instantiation	21, 22	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.modular.interval_left_shift_bijection
15	axiom		⊢
	proveit.logic.equality.substitution
16	instantiation	23, 24	⊢
	: , :
17	theorem		⊢
	proveit.numbers.modular.redundant_mod_elimination_in_sum_in_modabs
18	instantiation	73, 57, 25	⊢
	: , : , :
19	instantiation	73, 26, 27	⊢
	: , : , :
20	instantiation	28, 29, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.sets.functions.bijections.membership_unfolding
22	theorem		⊢
	proveit.physics.quantum.QPE._sample_space_bijection
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	instantiation	31, 61, 59	⊢
	: , :
25	instantiation	73, 60, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
27	instantiation	73, 33, 34	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	35, 36, 45, 72, 37, 38, 41, 42, 39	⊢
	: , : , : , : , : , :
30	instantiation	40, 41, 42, 43	⊢
	: , : , :
31	axiom		⊢
	proveit.physics.quantum.QPE._mod_add_def
32	instantiation	66, 61, 59	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
34	instantiation	44, 45, 46	⊢
	: , :
35	theorem		⊢
	proveit.numbers.addition.disassociation
36	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	instantiation	47	⊢
	: , :
39	instantiation	73, 49, 48	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
41	instantiation	73, 49, 55	⊢
	: , : , :
42	instantiation	73, 49, 50	⊢
	: , : , :
43	instantiation	51	⊢
	:
44	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
46	instantiation	73, 52, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48	instantiation	54, 55	⊢
	:
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	73, 57, 56	⊢
	: , : , :
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
53	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
54	theorem		⊢
	proveit.numbers.negation.real_closure
55	instantiation	73, 57, 58	⊢
	: , : , :
56	instantiation	73, 60, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
58	instantiation	73, 60, 61	⊢
	: , : , :
59	instantiation	73, 62, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
62	instantiation	64, 65, 70	⊢
	: , :
63	assumption		⊢
64	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
65	instantiation	66, 67, 68	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
67	instantiation	69, 70	⊢
	:
68	instantiation	73, 71, 72	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.negation.int_closure
70	instantiation	73, 74, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
75	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements