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	modus ponens	1, 2	, , , , , , , , , ⊢
1	instantiation	3, 86, 4, 5, 60, 6, 77	⊢
	: , : , : , : , : , : , : , :
2	instantiation	51, 7, 8	, , , , , , , , , ⊢
	: , : , :
3	theorem		⊢
	proveit.physics.quantum.algebra.qmult_distribution_over_summation
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
6	instantiation	35	⊢
	: , : , : , : , :
7	instantiation	9, 10, 11	, , , , , , , , , ⊢
	: , :
8	instantiation	58, 12, 13	⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_right_closure
10	assumption		⊢
11	instantiation	14, 15	, , , , , , , , ⊢
	:
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat7
13	instantiation	16	⊢
	: , : , : , : , : , : , :
14	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
15	instantiation	51, 17, 18	, , , , , , , , ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
17	instantiation	19, 20, 21	, , , , , , , , ⊢
	: , :
18	instantiation	58, 22, 23	⊢
	: , : , :
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
20	instantiation	51, 24, 25	, , , , , , , , ⊢
	: , : , :
21	instantiation	26, 73, 74	, ⊢
	: , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
23	instantiation	27	⊢
	: , : , : , : , : , :
24	instantiation	28, 29, 68, 30	, , , , , , , , ⊢
	: , : , :
25	instantiation	58, 31, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
29	instantiation	51, 33, 34	, , , , , , , ⊢
	: , : , :
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
32	instantiation	35	⊢
	: , : , : , : , :
33	instantiation	36, 55, 68, 37, 38	, , , , , , , ⊢
	: , : , : , :
34	instantiation	58, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
36	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
37	instantiation	61, 55, 68, 41	, , , , , , ⊢
	: , : , :
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
40	instantiation	42	⊢
	: , : , : , :
41	instantiation	51, 43, 44	, , , , , , ⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
43	instantiation	66, 45, 55, 68, 46	, , , , , , ⊢
	: , : , : , :
44	instantiation	58, 47, 48	⊢
	: , : , :
45	assumption		⊢
46	instantiation	61, 55, 68, 49	, , , , , ⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
48	instantiation	50	⊢
	: , : , :
49	instantiation	51, 52, 53	, , , , , ⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
51	theorem		⊢
	proveit.logic.equality.sub_left_side_into
52	instantiation	54, 55, 73, 68, 56, 57	, , , , , ⊢
	: , : , : , : , :
53	instantiation	58, 59, 60	⊢
	: , : , :
54	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
55	instantiation	78, 81	⊢
	:
56	instantiation	61, 73, 68, 62	, , ⊢
	: , : , :
57	instantiation	63, 80, 81, 64	, , , ⊢
	: , : , :
58	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
60	instantiation	65	⊢
	: , :
61	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
62	instantiation	66, 67, 73, 68, 69	, , ⊢
	: , : , : , :
63	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
64	modus ponens	70, 71	, , , ⊢
65	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
66	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
67	assumption		⊢
68	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
69	instantiation	72, 73, 74	, ⊢
	: , :
70	instantiation	75, 86, 76, 77	, , ⊢
	: , : , : , : , : , :
71	assumption		⊢
72	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
73	instantiation	78, 80	⊢
	:
74	assumption		⊢
75	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
76	instantiation	79, 80, 81	, ⊢
	: , :
77	instantiation	82, 83	⊢
	: , :
78	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
79	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
80	assumption		⊢
81	assumption		⊢
82	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
83	instantiation	84, 85, 86	⊢
	: , : , :
84	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
86	assumption		⊢