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.nat7
3	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
4	assumption		⊢
5	instantiation	8	⊢
	: , : , : , : , : , : , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	43, 9, 10	, , , , , , , , ⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
9	instantiation	11, 12, 13	, , , , , , , , ⊢
	: , :
10	instantiation	50, 14, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
12	instantiation	43, 16, 17	, , , , , , , , ⊢
	: , : , :
13	instantiation	18, 65, 66	, ⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
15	instantiation	19	⊢
	: , : , : , : , : , :
16	instantiation	20, 21, 60, 22	, , , , , , , , ⊢
	: , : , :
17	instantiation	50, 23, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
20	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
21	instantiation	43, 25, 26	, , , , , , , ⊢
	: , : , :
22	assumption		⊢
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
24	instantiation	27	⊢
	: , : , : , : , :
25	instantiation	28, 47, 60, 29, 30	, , , , , , , ⊢
	: , : , : , :
26	instantiation	50, 31, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
29	instantiation	53, 47, 60, 33	, , , , , , ⊢
	: , : , :
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
32	instantiation	34	⊢
	: , : , : , :
33	instantiation	43, 35, 36	, , , , , , ⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
35	instantiation	58, 37, 47, 60, 38	, , , , , , ⊢
	: , : , : , :
36	instantiation	50, 39, 40	⊢
	: , : , :
37	assumption		⊢
38	instantiation	53, 47, 60, 41	, , , , , ⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
40	instantiation	42	⊢
	: , : , :
41	instantiation	43, 44, 45	, , , , , ⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
43	theorem		⊢
	proveit.logic.equality.sub_left_side_into
44	instantiation	46, 47, 65, 60, 48, 49	, , , , , ⊢
	: , : , : , : , :
45	instantiation	50, 51, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
47	instantiation	70, 73	⊢
	:
48	instantiation	53, 65, 60, 54	, , ⊢
	: , : , :
49	instantiation	55, 72, 73, 56	, , , ⊢
	: , : , :
50	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
51	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
52	instantiation	57	⊢
	: , :
53	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
54	instantiation	58, 59, 65, 60, 61	, , ⊢
	: , : , : , :
55	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
56	modus ponens	62, 63	, , , ⊢
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
58	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
59	assumption		⊢
60	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
61	instantiation	64, 65, 66	, ⊢
	: , :
62	instantiation	67, 78, 68, 69	, , ⊢
	: , : , : , : , : , :
63	assumption		⊢
64	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
65	instantiation	70, 72	⊢
	:
66	assumption		⊢
67	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
68	instantiation	71, 72, 73	, ⊢
	: , :
69	instantiation	74, 75	⊢
	: , :
70	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
71	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
72	assumption		⊢
73	assumption		⊢
74	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
75	instantiation	76, 77, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
78	assumption		⊢