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