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.strong_bound_via_left_term_bound
2	reference	44	⊢
3	instantiation	7, 33, 54	⊢
	: , :
4	instantiation	8, 44, 33, 54, 9, 10	⊢
	: , : , :
5	instantiation	11, 27, 12, 13	⊢
	: , : , :
6	instantiation	47, 14, 15	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
9	instantiation	16, 44, 54, 45	⊢
	: , : , :
10	instantiation	17, 68	⊢
	:
11	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
12	instantiation	82, 69, 18	⊢
	: , : , :
13	instantiation	19, 35, 81, 20^*	⊢
	: , : , : , :
14	instantiation	21, 22, 84, 46, 23, 24, 28, 27, 25	⊢
	: , : , : , : , : , :
15	instantiation	26, 27, 28, 29	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
17	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
18	instantiation	82, 75, 30	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
20	instantiation	47, 31, 32	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.disassociation
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	62	⊢
	: , :
25	instantiation	82, 69, 44	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
27	instantiation	82, 69, 54	⊢
	: , : , :
28	instantiation	82, 69, 33	⊢
	: , : , :
29	instantiation	34	⊢
	:
30	instantiation	82, 80, 35	⊢
	: , : , :
31	instantiation	55, 84, 36, 37, 38, 39	⊢
	: , : , : , :
32	instantiation	40, 41, 42	⊢
	:
33	instantiation	43, 44, 54, 45	⊢
	: , : , :
34	axiom		⊢
	proveit.logic.equality.equals_reflexivity
35	instantiation	82, 83, 46	⊢
	: , : , :
36	instantiation	62	⊢
	: , :
37	instantiation	62	⊢
	: , :
38	instantiation	47, 48, 49	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
40	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
41	instantiation	82, 69, 50	⊢
	: , : , :
42	instantiation	51, 52	⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
44	instantiation	53, 54	⊢
	:
45	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
47	axiom		⊢
	proveit.logic.equality.equals_transitivity
48	instantiation	55, 84, 56, 57, 58, 59	⊢
	: , : , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
50	instantiation	82, 75, 60	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
53	theorem		⊢
	proveit.numbers.negation.real_closure
54	instantiation	82, 75, 61	⊢
	: , : , :
55	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
56	instantiation	62	⊢
	: , :
57	instantiation	62	⊢
	: , :
58	instantiation	63, 65	⊢
	:
59	instantiation	64, 65	⊢
	:
60	instantiation	82, 80, 66	⊢
	: , : , :
61	instantiation	82, 67, 68	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
64	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
65	instantiation	82, 69, 70	⊢
	: , : , :
66	instantiation	82, 83, 71	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
68	instantiation	72, 73, 74	⊢
	: , :
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
70	instantiation	82, 75, 76	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
72	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
73	instantiation	82, 78, 77	⊢
	: , : , :
74	instantiation	82, 78, 79	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	82, 80, 81	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
78	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
79	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
81	instantiation	82, 83, 84	⊢
	: , : , :
82	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
84	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements