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