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	, , , , , , , , , ⊢
	: , : , :
1	reference	46	⊢
2	instantiation	4, 5, 6	, , , , , , , , , ⊢
	: , :
3	instantiation	53, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_right_closure
5	assumption		⊢
6	instantiation	9, 10	, , , , , , , , ⊢
	:
7	theorem		⊢
	proveit.numbers.numerals.decimals.posnat7
8	instantiation	11	⊢
	: , : , : , : , : , : , :
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
10	instantiation	46, 12, 13	, , , , , , , , ⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
12	instantiation	14, 15, 16	, , , , , , , , ⊢
	: , :
13	instantiation	53, 17, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
15	instantiation	46, 19, 20	, , , , , , , , ⊢
	: , : , :
16	instantiation	21, 68, 69	, ⊢
	: , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
18	instantiation	22	⊢
	: , : , : , : , : , :
19	instantiation	23, 24, 63, 25	, , , , , , , , ⊢
	: , : , :
20	instantiation	53, 26, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
23	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
24	instantiation	46, 28, 29	, , , , , , , ⊢
	: , : , :
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
27	instantiation	30	⊢
	: , : , : , : , :
28	instantiation	31, 50, 63, 32, 33	, , , , , , , ⊢
	: , : , : , :
29	instantiation	53, 34, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
31	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
32	instantiation	56, 50, 63, 36	, , , , , , ⊢
	: , : , :
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
35	instantiation	37	⊢
	: , : , : , :
36	instantiation	46, 38, 39	, , , , , , ⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
38	instantiation	61, 40, 50, 63, 41	, , , , , , ⊢
	: , : , : , :
39	instantiation	53, 42, 43	⊢
	: , : , :
40	assumption		⊢
41	instantiation	56, 50, 63, 44	, , , , , ⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
43	instantiation	45	⊢
	: , : , :
44	instantiation	46, 47, 48	, , , , , ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
46	theorem		⊢
	proveit.logic.equality.sub_left_side_into
47	instantiation	49, 50, 68, 63, 51, 52	, , , , , ⊢
	: , : , : , : , :
48	instantiation	53, 54, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
50	instantiation	73, 76	⊢
	:
51	instantiation	56, 68, 63, 57	, , ⊢
	: , : , :
52	instantiation	58, 75, 76, 59	, , , ⊢
	: , : , :
53	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
55	instantiation	60	⊢
	: , :
56	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
57	instantiation	61, 62, 68, 63, 64	, , ⊢
	: , : , : , :
58	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
59	modus ponens	65, 66	, , , ⊢
60	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
61	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
62	assumption		⊢
63	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
64	instantiation	67, 68, 69	, ⊢
	: , :
65	instantiation	70, 81, 71, 72	, , ⊢
	: , : , : , : , : , :
66	assumption		⊢
67	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
68	instantiation	73, 75	⊢
	:
69	assumption		⊢
70	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
71	instantiation	74, 75, 76	, ⊢
	: , :
72	instantiation	77, 78	⊢
	: , :
73	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
74	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
75	assumption		⊢
76	assumption		⊢
77	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
78	instantiation	79, 80, 81	⊢
	: , : , :
79	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
81	assumption		⊢