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