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	, ⊢
	: , :
1	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
3	instantiation	6	⊢
	: , :
4	instantiation	58, 8, 7	⊢
	: , : , :
5	instantiation	58, 8, 9	, ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
7	instantiation	58, 10, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
9	instantiation	58, 12, 13	, ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
11	instantiation	58, 14, 15	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
13	instantiation	16, 17	, ⊢
	:
14	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
15	instantiation	58, 18, 19	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
17	instantiation	20, 21, 22	, ⊢
	:
18	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
21	instantiation	58, 23, 24	⊢
	: , : , :
22	instantiation	25, 26	, ⊢
	: , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	27, 28, 29	⊢
	: , :
25	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
26	instantiation	30, 31, 46, 32	, ⊢
	: , :
27	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
28	instantiation	33, 34, 35, 36	⊢
	: , : , :
29	instantiation	37, 38	⊢
	:
30	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
31	instantiation	39, 40, 57, 41	⊢
	: , : , : , : , :
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
35	instantiation	58, 43, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
37	theorem		⊢
	proveit.numbers.negation.real_closure
38	instantiation	58, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
40	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
41	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
42	instantiation	58, 45, 53	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	58, 45, 46	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	58, 47, 48	⊢
	: , : , :
47	instantiation	49, 50, 55	⊢
	: , :
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
50	instantiation	51, 52, 53	⊢
	: , :
51	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
52	instantiation	54, 55	⊢
	:
53	instantiation	58, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.negation.int_closure
55	instantiation	58, 59, 60	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
58	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
60	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos