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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 9, 10^*	, ⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	11, 67, 70, 12, 13, 14, 22, 15, 16	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.division.frac_cancel_left
7	instantiation	68, 18, 17	⊢
	: , : , :
8	instantiation	68, 18, 19	⊢
	: , : , :
9	instantiation	68, 46, 20	, ⊢
	: , : , :
10	instantiation	21, 22	⊢
	:
11	theorem		⊢
	proveit.numbers.multiplication.association
12	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
13	instantiation	23	⊢
	: , :
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15	instantiation	68, 46, 37	⊢
	: , : , :
16	instantiation	68, 46, 24	⊢
	: , : , :
17	instantiation	68, 26, 25	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19	instantiation	68, 26, 27	⊢
	: , : , :
20	instantiation	28, 29, 30, 31	, ⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
22	instantiation	68, 46, 57	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
24	instantiation	68, 32, 33	⊢
	: , : , :
25	instantiation	68, 35, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27	instantiation	68, 35, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
30	instantiation	55, 37, 57, 58	⊢
	: , :
31	instantiation	38, 54, 39	, ⊢
	:
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
33	instantiation	40, 41	⊢
	:
34	instantiation	68, 42, 63	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36	instantiation	68, 42, 43	⊢
	: , : , :
37	instantiation	68, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
41	instantiation	68, 46, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	48, 49, 52, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
49	instantiation	51, 52	⊢
	:
50	instantiation	53, 54	⊢
	:
51	theorem		⊢
	proveit.numbers.negation.real_closure
52	instantiation	55, 56, 57, 58	⊢
	: , :
53	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.division.div_real_closure
56	instantiation	68, 60, 59	⊢
	: , : , :
57	instantiation	68, 60, 61	⊢
	: , : , :
58	instantiation	62, 63	⊢
	:
59	instantiation	68, 65, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	68, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
64	instantiation	68, 69, 67	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	68, 69, 70	⊢
	: , : , :
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_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements