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	, , , , , , , , ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
4	assumption		⊢
5	reference	23	⊢
6	instantiation	65	⊢
	: , :
7	instantiation	49, 8, 9	, , , , , , , ⊢
	: , : , :
8	instantiation	10, 11, 12	, , , , , , , ⊢
	: , :
9	instantiation	55, 13, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
11	instantiation	49, 15, 16	, , , , , , , ⊢
	: , : , :
12	instantiation	17, 63, 64	, ⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
14	instantiation	18	⊢
	: , : , : , : , : , :
15	instantiation	19, 29, 60, 20, 21	, , , , , , , ⊢
	: , : , : , :
16	instantiation	55, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
20	instantiation	46, 29, 60, 24	, , , , , , ⊢
	: , : , :
21	assumption		⊢
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
23	instantiation	25	⊢
	: , : , : , : , :
24	instantiation	49, 26, 27	, , , , , , ⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
26	instantiation	28, 29, 63, 60, 30, 31	, , , , , , ⊢
	: , : , : , : , :
27	instantiation	55, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
29	instantiation	66, 36	⊢
	:
30	instantiation	46, 63, 60, 34	, , , , ⊢
	: , : , :
31	instantiation	35, 67, 36, 37	, , ⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
33	instantiation	38	⊢
	: , : , : , :
34	instantiation	49, 39, 40	, , , , ⊢
	: , : , :
35	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
36	assumption		⊢
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
39	instantiation	41, 42, 63, 60, 43	, , , , ⊢
	: , : , : , :
40	instantiation	55, 44, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
42	assumption		⊢
43	instantiation	46, 63, 60, 47	, , , ⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
45	instantiation	48	⊢
	: , : , :
46	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
47	instantiation	49, 50, 51	, , , ⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
49	theorem		⊢
	proveit.logic.equality.sub_left_side_into
50	instantiation	52, 53, 63, 60, 54	, , , ⊢
	: , : , : , :
51	instantiation	55, 56, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
53	instantiation	58, 59, 60, 61	, ⊢
	: , : , :
54	instantiation	62, 63, 64	, ⊢
	: , :
55	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
57	instantiation	65	⊢
	: , :
58	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
59	assumption		⊢
60	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
61	assumption		⊢
62	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
63	instantiation	66, 67	⊢
	:
64	assumption		⊢
65	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
66	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
67	assumption		⊢