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