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	reference	45	⊢
2	instantiation	4, 5, 6	, , , , , , , , ⊢
	: , :
3	instantiation	58, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
5	instantiation	45, 9, 10	, , , , , , , , ⊢
	: , : , :
6	instantiation	11, 49, 50	, ⊢
	: , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
8	instantiation	12	⊢
	: , : , : , : , : , :
9	instantiation	13, 23, 68, 14, 15	, , , , , , , , ⊢
	: , : , : , :
10	instantiation	58, 16, 17	⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
13	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
14	instantiation	28, 23, 68, 18	, , , , , , , ⊢
	: , : , :
15	assumption		⊢
16	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
17	instantiation	19	⊢
	: , : , : , : , :
18	instantiation	45, 20, 21	, , , , , , , ⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
20	instantiation	22, 23, 49, 68, 24, 25	, , , , , , , ⊢
	: , : , : , : , :
21	instantiation	58, 26, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
23	instantiation	61, 53	⊢
	:
24	instantiation	28, 49, 68, 29	, , , , ⊢
	: , : , :
25	instantiation	30, 62, 53, 31	, , , ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
27	instantiation	32	⊢
	: , : , : , :
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
29	instantiation	45, 33, 34	, , , , ⊢
	: , : , :
30	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
31	modus ponens	35, 36	, , , ⊢
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
33	instantiation	37, 38, 49, 68, 39	, , , , ⊢
	: , : , : , :
34	instantiation	58, 40, 41	⊢
	: , : , :
35	instantiation	42, 65, 43, 44	, , ⊢
	: , : , : , : , : , :
36	assumption		⊢
37	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
38	instantiation	45, 46, 47	, , ⊢
	: , : , :
39	instantiation	48, 49, 50	, ⊢
	: , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
41	instantiation	51	⊢
	: , : , :
42	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
43	instantiation	52, 62, 53	, ⊢
	: , :
44	instantiation	54, 55	⊢
	: , :
45	theorem		⊢
	proveit.logic.equality.sub_left_side_into
46	instantiation	66, 56, 68, 57	, , ⊢
	: , : , :
47	instantiation	58, 59, 60	⊢
	: , : , :
48	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
49	instantiation	61, 62	⊢
	:
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
52	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
53	assumption		⊢
54	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
55	instantiation	63, 64, 65	⊢
	: , : , :
56	instantiation	66, 67, 68, 69	, ⊢
	: , : , :
57	assumption		⊢
58	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
60	instantiation	70	⊢
	: , :
61	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
62	assumption		⊢
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
65	assumption		⊢
66	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
67	assumption		⊢
68	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
69	assumption		⊢
70	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq