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