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