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