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, 75, 8, 7, 10, 9, 5, 11, 12, 13	⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 8, 9, 10, 11, 12, 13	⊢
	: , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.disassociation
5	instantiation	76, 44, 20	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	instantiation	14	⊢
	: , : , :
11	instantiation	76, 44, 15	⊢
	: , : , :
12	instantiation	76, 44, 48	⊢
	: , : , :
13	instantiation	16, 17, 18	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
15	instantiation	19, 20, 21, 22	⊢
	: , :
16	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
17	instantiation	76, 44, 23	⊢
	: , : , :
18	instantiation	76, 44, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.division.div_real_closure
20	instantiation	76, 50, 25	⊢
	: , : , :
21	instantiation	76, 50, 26	⊢
	: , : , :
22	instantiation	27, 70	⊢
	:
23	instantiation	76, 28, 29	⊢
	: , : , :
24	instantiation	76, 50, 30	⊢
	: , : , :
25	instantiation	76, 52, 68	⊢
	: , : , :
26	instantiation	76, 52, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
29	instantiation	32, 33	⊢
	:
30	instantiation	76, 52, 34	⊢
	: , : , :
31	instantiation	76, 74, 35	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
33	instantiation	36, 37, 38	⊢
	: , :
34	instantiation	72, 68	⊢
	:
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
36	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
37	instantiation	76, 44, 39	⊢
	: , : , :
38	instantiation	40, 41	⊢
	:
39	instantiation	42, 43	⊢
	:
40	theorem		⊢
	proveit.numbers.negation.complex_closure
41	instantiation	76, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
43	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	46, 47, 48	⊢
	: , :
46	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
47	instantiation	76, 50, 49	⊢
	: , : , :
48	instantiation	76, 50, 51	⊢
	: , : , :
49	instantiation	76, 52, 53	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	76, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	76, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
55	instantiation	58, 59, 60	⊢
	: , :
56	instantiation	61, 62, 73	⊢
	: , :
57	assumption		⊢
58	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
59	instantiation	76, 63, 64	⊢
	: , : , :
60	instantiation	72, 65	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
62	instantiation	66, 67, 68	⊢
	: , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
64	instantiation	76, 69, 70	⊢
	: , : , :
65	instantiation	76, 77, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
67	instantiation	72, 73	⊢
	:
68	instantiation	76, 74, 75	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
71	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
72	theorem		⊢
	proveit.numbers.negation.int_closure
73	instantiation	76, 77, 78	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
78	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos