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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	9, 4, 5, 95, 6, 7, 8	, , , , , , , , ,  ⊢
	: , : , : , : , :
3	instantiation	9, 10, 11, 33, 24, 12	, , , , , , , , ,  ⊢
	: , : , : , : , :
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat7
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	instantiation	13	⊢
	: , : , : , : , : , : , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	74, 14, 15	, , , , , , , ,  ⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
12	instantiation	74, 16, 17	, , , , , , , ,  ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
14	instantiation	20, 18, 22	, , , , , , , ,  ⊢
	: , :
15	instantiation	81, 23, 19	⊢
	: , : , :
16	instantiation	20, 21, 22	, , , , , , , ,  ⊢
	: , :
17	instantiation	81, 23, 24	⊢
	: , : , :
18	instantiation	74, 25, 26	, , , , , , , ,  ⊢
	: , : , :
19	instantiation	30	⊢
	: , : , : , : , : , :
20	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
21	instantiation	74, 27, 28	, , , , , , , ,  ⊢
	: , : , :
22	instantiation	29, 103, 104	,  ⊢
	: , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
24	instantiation	30	⊢
	: , : , : , : , : , :
25	instantiation	31, 32, 96, 33	, , , , , , , ,  ⊢
	: , : , :
26	instantiation	81, 36, 34	⊢
	: , : , :
27	instantiation	42, 70, 96, 35, 44	, , , , , , , ,  ⊢
	: , : , : , :
28	instantiation	81, 36, 37	⊢
	: , : , :
29	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
31	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
32	instantiation	74, 38, 39	, , , , , , ,  ⊢
	: , : , :
33	assumption		⊢
34	instantiation	41	⊢
	: , : , : , : , :
35	instantiation	88, 70, 96, 40	, , , , , , ,  ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
37	instantiation	41	⊢
	: , : , : , : , :
38	instantiation	42, 70, 96, 43, 44	, , , , , , ,  ⊢
	: , : , : , :
39	instantiation	81, 50, 45	⊢
	: , : , :
40	instantiation	74, 46, 47	, , , , , , ,  ⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
42	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
43	instantiation	88, 70, 96, 48	, , , , , ,  ⊢
	: , : , :
44	assumption		⊢
45	instantiation	55	⊢
	: , : , : , :
46	instantiation	84, 56, 70, 96, 49	, , , , , , ,  ⊢
	: , : , : , :
47	instantiation	81, 50, 51	⊢
	: , : , :
48	instantiation	74, 52, 53	, , , , , ,  ⊢
	: , : , :
49	instantiation	88, 70, 96, 54	, , , , , ,  ⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
51	instantiation	55	⊢
	: , : , : , :
52	instantiation	84, 56, 70, 96, 57	, , , , , ,  ⊢
	: , : , : , :
53	instantiation	81, 63, 58	⊢
	: , : , :
54	instantiation	74, 59, 60	, , , , , ,  ⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
56	assumption		⊢
57	instantiation	88, 70, 96, 61	, , , , ,  ⊢
	: , : , :
58	instantiation	68	⊢
	: , : , :
59	instantiation	69, 70, 103, 96, 62, 72	, , , , , ,  ⊢
	: , : , : , : , :
60	instantiation	81, 63, 64	⊢
	: , : , :
61	instantiation	74, 65, 66	, , , , ,  ⊢
	: , : , :
62	instantiation	88, 103, 96, 67	, , ,  ⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
64	instantiation	68	⊢
	: , : , :
65	instantiation	69, 70, 103, 96, 71, 72	, , , , ,  ⊢
	: , : , : , : , :
66	instantiation	81, 82, 73	⊢
	: , : , :
67	instantiation	74, 75, 76	, , ,  ⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
69	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
70	instantiation	108, 99	⊢
	:
71	instantiation	88, 103, 96, 77	, ,  ⊢
	: , : , :
72	instantiation	78, 109, 99, 79	, , ,  ⊢
	: , : , :
73	instantiation	90	⊢
	: , :
74	theorem		⊢
	proveit.logic.equality.sub_left_side_into
75	instantiation	84, 85, 103, 96, 80	, , ,  ⊢
	: , : , : , :
76	instantiation	81, 82, 83	⊢
	: , : , :
77	instantiation	84, 85, 103, 96, 97	, ,  ⊢
	: , : , : , :
78	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
79	modus ponens	86, 87	, , ,  ⊢
80	instantiation	88, 103, 96, 89	, ,  ⊢
	: , : , :
81	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
82	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
83	instantiation	90	⊢
	: , :
84	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
85	assumption		⊢
86	instantiation	91, 107, 92, 93	, ,  ⊢
	: , : , : , : , : , :
87	assumption		⊢
88	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
89	instantiation	94, 95, 103, 96, 97	, ,  ⊢
	: , : , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
91	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
92	instantiation	98, 109, 99	,  ⊢
	: , :
93	instantiation	100, 101	⊢
	: , :
94	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
95	assumption		⊢
96	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
97	instantiation	102, 103, 104	,  ⊢
	: , :
98	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
99	assumption		⊢
100	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
101	instantiation	105, 106, 107	⊢
	: , : , :
102	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
103	instantiation	108, 109	⊢
	:
104	assumption		⊢
105	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
106	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
107	assumption		⊢
108	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
109	assumption		⊢