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	, , , , , , , , ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
4	assumption		⊢
5	reference	13	⊢
6	instantiation	46, 7, 8	, , , , , , , ⊢
	: , : , :
7	instantiation	9, 10, 11	, , , , , , , ⊢
	: , :
8	instantiation	52, 12, 13	⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
10	instantiation	46, 14, 15	, , , , , , , ⊢
	: , : , :
11	instantiation	16, 63, 64	, ⊢
	: , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
13	instantiation	17	⊢
	: , : , : , : , : , :
14	instantiation	18, 36, 60, 19, 20	, , , , , , , ⊢
	: , : , : , :
15	instantiation	52, 21, 22	⊢
	: , : , :
16	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
18	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
19	instantiation	55, 36, 60, 23	, , , , , , ⊢
	: , : , :
20	assumption		⊢
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
22	instantiation	24	⊢
	: , : , : , : , :
23	instantiation	46, 25, 26	, , , , , , ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
25	instantiation	49, 27, 36, 60, 28	, , , , , , ⊢
	: , : , : , :
26	instantiation	52, 29, 30	⊢
	: , : , :
27	assumption		⊢
28	instantiation	55, 36, 60, 31	, , , , , ⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
30	instantiation	32	⊢
	: , : , : , :
31	instantiation	46, 33, 34	, , , , , ⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
33	instantiation	35, 36, 63, 60, 37, 38	, , , , , ⊢
	: , : , : , : , :
34	instantiation	52, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
36	instantiation	65, 43	⊢
	:
37	instantiation	55, 63, 60, 41	, , , ⊢
	: , : , :
38	instantiation	42, 66, 43, 44	, , ⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
40	instantiation	45	⊢
	: , : , :
41	instantiation	46, 47, 48	, , , ⊢
	: , : , :
42	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
43	assumption		⊢
44	assumption		⊢
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
46	theorem		⊢
	proveit.logic.equality.sub_left_side_into
47	instantiation	49, 50, 63, 60, 51	, , , ⊢
	: , : , : , :
48	instantiation	52, 53, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
50	assumption		⊢
51	instantiation	55, 63, 60, 56	, , ⊢
	: , : , :
52	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
54	instantiation	57	⊢
	: , :
55	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
56	instantiation	58, 59, 63, 60, 61	, , ⊢
	: , : , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
58	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
59	assumption		⊢
60	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
61	instantiation	62, 63, 64	, ⊢
	: , :
62	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
63	instantiation	65, 66	⊢
	:
64	assumption		⊢
65	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
66	assumption		⊢