Show the Proof

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

	step type	requirements	statement
0	instantiation	1, 2, 3	, , , , , ,  ⊢
	: , : , :
1	reference	4	⊢
2	instantiation	4, 5, 6	, , , , , ,  ⊢
	: , : , :
3	instantiation	15, 7, 63, 47, 8, 9	, , , , , ,  ⊢
	: , : , : , : , :
4	axiom		⊢
	proveit.logic.equality.equals_transitivity
5	instantiation	15, 10, 11, 59, 12, 13, 14	, , , , , ,  ⊢
	: , : , : , : , :
6	instantiation	15, 16, 17, 55, 34, 18	, , , , , ,  ⊢
	: , : , : , : , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
8	instantiation	61	⊢
	: , :
9	instantiation	43, 19, 20	, , , , ,  ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	instantiation	21	⊢
	: , : , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	43, 22, 23	, , , , ,  ⊢
	: , : , :
15	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
18	instantiation	43, 24, 25	, , , , ,  ⊢
	: , : , :
19	instantiation	30, 64, 65, 26, 32	, , , , ,  ⊢
	: , : , : , :
20	instantiation	52, 33, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
22	instantiation	30, 64, 65, 28, 32	, , , , ,  ⊢
	: , : , : , :
23	instantiation	52, 33, 29	⊢
	: , : , :
24	instantiation	30, 64, 65, 31, 32	, , , , ,  ⊢
	: , : , : , :
25	instantiation	52, 33, 34	⊢
	: , : , :
26	instantiation	56, 64, 65, 35	, , , ,  ⊢
	: , : , :
27	instantiation	38	⊢
	: , : , :
28	instantiation	56, 64, 65, 36	, , , ,  ⊢
	: , : , :
29	instantiation	38	⊢
	: , : , :
30	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
31	instantiation	56, 64, 65, 37	, , , ,  ⊢
	: , : , :
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
34	instantiation	38	⊢
	: , : , :
35	instantiation	43, 39, 40	, , , ,  ⊢
	: , : , :
36	instantiation	43, 41, 42	, , , ,  ⊢
	: , : , :
37	instantiation	43, 44, 45	, , , ,  ⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
39	instantiation	62, 46, 64, 65, 66	, , , ,  ⊢
	: , : , : , :
40	instantiation	52, 53, 47	⊢
	: , : , :
41	instantiation	48, 55, 64, 65, 49	, , , ,  ⊢
	: , : , : , :
42	instantiation	52, 53, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.equality.sub_left_side_into
44	instantiation	62, 51, 64, 65, 66	, , , ,  ⊢
	: , : , : , :
45	instantiation	52, 53, 54	⊢
	: , : , :
46	instantiation	58, 55, 60, 59	,  ⊢
	: , : , :
47	instantiation	61	⊢
	: , :
48	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
49	instantiation	56, 64, 65, 57	, , ,  ⊢
	: , : , :
50	instantiation	61	⊢
	: , :
51	instantiation	58, 59, 60, 63	,  ⊢
	: , : , :
52	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
54	instantiation	61	⊢
	: , :
55	assumption		⊢
56	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
57	instantiation	62, 63, 64, 65, 66	, , ,  ⊢
	: , : , : , :
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	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
62	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
63	assumption		⊢
64	instantiation	67, 70	⊢
	:
65	instantiation	67, 69	⊢
	:
66	instantiation	68, 69, 70, 71	, ,  ⊢
	: , : , :
67	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
68	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
69	assumption		⊢
70	assumption		⊢
71	assumption		⊢