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