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.addition.weak_bound_via_left_term_bound
2	reference	22	⊢
3	instantiation	7, 27, 24	⊢
	: , :
4	instantiation	29, 30, 8	⊢
	: , : , :
5	axiom		⊢
	proveit.physics.quantum.QPE._t_req
6	instantiation	9, 10, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	12, 13, 48, 77, 14, 15, 18, 19, 16	⊢
	: , : , : , : , : , :
11	instantiation	17, 18, 19, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.disassociation
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15	instantiation	21	⊢
	: , :
16	instantiation	75, 23, 22	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
18	instantiation	75, 23, 27	⊢
	: , : , :
19	instantiation	75, 23, 24	⊢
	: , : , :
20	instantiation	25	⊢
	:
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22	instantiation	26, 27	⊢
	:
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	75, 71, 28	⊢
	: , : , :
25	axiom		⊢
	proveit.logic.equality.equals_reflexivity
26	theorem		⊢
	proveit.numbers.negation.real_closure
27	instantiation	29, 30, 31	⊢
	: , : , :
28	instantiation	75, 73, 32	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
30	instantiation	33, 34	⊢
	: , :
31	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
32	instantiation	35, 36	⊢
	:
33	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
35	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
36	instantiation	37, 57, 38, 39	⊢
	: , :
37	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
38	instantiation	40, 57, 41	⊢
	: , :
39	instantiation	42, 43	⊢
	: , :
40	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
41	instantiation	44, 45, 55, 46	⊢
	: , :
42	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
43	instantiation	47, 77, 48, 49	⊢
	: , :
44	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
45	instantiation	75, 59, 50	⊢
	: , : , :
46	instantiation	51, 52	⊢
	:
47	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
49	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
50	instantiation	75, 64, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
52	instantiation	75, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
55	instantiation	56, 57, 58	⊢
	: , :
56	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
57	instantiation	75, 59, 60	⊢
	: , : , :
58	instantiation	61, 62, 63	⊢
	:
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
60	instantiation	75, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
62	instantiation	66, 68, 69, 70	⊢
	: , : , :
63	instantiation	67, 68, 69, 70	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
69	instantiation	75, 71, 72	⊢
	: , : , :
70	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
72	instantiation	75, 73, 74	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	instantiation	75, 76, 77	⊢
	: , : , :
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements