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