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