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	, ⊢
	:
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
2	instantiation	68, 3, 4	, ⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
4	instantiation	5, 10, 6	, ⊢
	:
5	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
6	instantiation	7, 8	, ⊢
	: , :
7	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
8	instantiation	9, 31, 10, 11	, ⊢
	: , :
9	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
10	instantiation	12, 13, 14	, ⊢
	: , :
11	instantiation	15, 16	, ⊢
	: , :
12	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
13	instantiation	68, 56, 17	, ⊢
	: , : , :
14	instantiation	18, 19	⊢
	:
15	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
16	instantiation	20, 21, 22	, ⊢
	: , : , :
17	instantiation	68, 61, 23	, ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.negation.real_closure
19	instantiation	24, 31, 53, 26	⊢
	: , : , :
20	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
21	instantiation	25, 31, 53, 26	⊢
	: , : , :
22	instantiation	38, 27, 28	, ⊢
	: , : , :
23	instantiation	68, 29, 35	, ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
26	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
27	instantiation	30, 53, 31, 32, 33, 34^*	⊢
	: , : , :
28	instantiation	45, 36, 59, 35	, ⊢
	: , : , :
29	instantiation	54, 36, 59	⊢
	: , :
30	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
32	instantiation	68, 56, 37	⊢
	: , : , :
33	instantiation	38, 39, 40	⊢
	: , : , :
34	instantiation	41, 42, 43	⊢
	: , : , :
35	assumption		⊢
36	instantiation	58, 44, 62	⊢
	: , :
37	instantiation	68, 61, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
39	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
40	instantiation	45, 62, 55, 51	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.equality.sub_right_side_into
42	instantiation	46, 48	⊢
	:
43	instantiation	47, 48, 49	⊢
	: , :
44	instantiation	68, 50, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
46	theorem		⊢
	proveit.numbers.addition.elim_zero_right
47	theorem		⊢
	proveit.numbers.addition.commutation
48	instantiation	68, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
50	instantiation	54, 62, 55	⊢
	: , :
51	assumption		⊢
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	instantiation	68, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
55	instantiation	58, 59, 60	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	68, 61, 62	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
59	instantiation	68, 63, 64	⊢
	: , : , :
60	instantiation	65, 66	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	68, 69, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
64	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
65	theorem		⊢
	proveit.numbers.negation.int_closure
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