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	, , , , , , , , ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_association
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
3	reference	49	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	reference	34	⊢
6	instantiation	52	⊢
	: , : , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	53, 9, 10	, , , , , , , , ⊢
	: , : , :
9	instantiation	11, 12, 13	, , , , , , , , ⊢
	: , :
10	instantiation	60, 14, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_right_closure
12	assumption		⊢
13	instantiation	16, 17	, , , , , , , ⊢
	:
14	theorem		⊢
	proveit.numbers.numerals.decimals.posnat7
15	instantiation	18	⊢
	: , : , : , : , : , : , :
16	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
17	instantiation	53, 19, 20	, , , , , , , ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
19	instantiation	21, 22, 23	, , , , , , , ⊢
	: , :
20	instantiation	60, 24, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
22	instantiation	53, 26, 27	, , , , , , , ⊢
	: , : , :
23	instantiation	28, 74, 75	, ⊢
	: , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
25	instantiation	29	⊢
	: , : , : , : , : , :
26	instantiation	30, 31, 71, 32	, , , , , , , ⊢
	: , : , :
27	instantiation	60, 33, 34	⊢
	: , : , :
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
30	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
31	instantiation	53, 35, 36	, , , , , , ⊢
	: , : , :
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
34	instantiation	37	⊢
	: , : , : , : , :
35	instantiation	38, 57, 71, 39, 40	, , , , , , ⊢
	: , : , : , :
36	instantiation	60, 41, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
38	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
39	instantiation	63, 57, 71, 43	, , , , , ⊢
	: , : , :
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
42	instantiation	44	⊢
	: , : , : , :
43	instantiation	53, 45, 46	, , , , , ⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
45	instantiation	69, 47, 57, 71, 48	, , , , , ⊢
	: , : , : , :
46	instantiation	60, 49, 50	⊢
	: , : , :
47	assumption		⊢
48	instantiation	63, 57, 71, 51	, , , , ⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
50	instantiation	52	⊢
	: , : , :
51	instantiation	53, 54, 55	, , , , ⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
53	theorem		⊢
	proveit.logic.equality.sub_left_side_into
54	instantiation	56, 57, 74, 71, 58, 59	, , , , ⊢
	: , : , : , : , :
55	instantiation	60, 61, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
57	instantiation	76, 66	⊢
	:
58	instantiation	63, 74, 71, 64	, , ⊢
	: , : , :
59	instantiation	65, 77, 66, 67	, , ⊢
	: , : , :
60	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
62	instantiation	68	⊢
	: , :
63	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
64	instantiation	69, 70, 74, 71, 72	, , ⊢
	: , : , : , :
65	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
66	assumption		⊢
67	assumption		⊢
68	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
69	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
70	assumption		⊢
71	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
72	instantiation	73, 74, 75	, ⊢
	: , :
73	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
74	instantiation	76, 77	⊢
	:
75	assumption		⊢
76	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
77	assumption		⊢