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, 7, 8, 9, 10^, 11^	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
2	reference	67	⊢
3	reference	28	⊢
4	reference	27	⊢
5	instantiation	36	⊢
	: , :
6	reference	29	⊢
7	reference	25	⊢
8	instantiation	12, 14	⊢
	:
9	reference	17	⊢
10	instantiation	13, 25, 14, 15^*	⊢
	: , :
11	instantiation	16, 17	⊢
	:
12	theorem		⊢
	proveit.numbers.negation.complex_closure
13	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
14	instantiation	68, 38, 18	⊢
	: , : , :
15	instantiation	19, 20, 21	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
17	instantiation	68, 38, 22	⊢
	: , : , :
18	instantiation	23, 37, 39	⊢
	: , :
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	24, 67, 28, 27, 30, 29, 25, 31, 32	⊢
	: , : , : , : , : , :
21	instantiation	26, 27, 28, 29, 30, 31, 32	⊢
	: , : , : , :
22	instantiation	33, 34	⊢
	:
23	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
24	theorem		⊢
	proveit.numbers.multiplication.disassociation
25	instantiation	68, 38, 35	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	36	⊢
	: , :
31	instantiation	68, 38, 37	⊢
	: , : , :
32	instantiation	68, 38, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
34	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
35	instantiation	68, 42, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	instantiation	68, 42, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	68, 42, 43	⊢
	: , : , :
40	instantiation	68, 44, 60	⊢
	: , : , :
41	instantiation	68, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	68, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
45	instantiation	68, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
47	instantiation	50, 51, 52	⊢
	: , :
48	instantiation	53, 54, 65	⊢
	: , :
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
51	instantiation	68, 55, 56	⊢
	: , : , :
52	instantiation	64, 57	⊢
	:
53	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
54	instantiation	58, 59, 60	⊢
	: , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
56	instantiation	68, 61, 62	⊢
	: , : , :
57	instantiation	68, 69, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
59	instantiation	64, 65	⊢
	:
60	instantiation	68, 66, 67	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
63	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	68, 69, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
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_pos_within_int
70	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements