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	35, 4, 5	, , , , , , , ⊢
	: , : , :
3	instantiation	6, 52, 53	, ⊢
	: , :
4	instantiation	7, 25, 49, 8, 9	, , , , , , , ⊢
	: , : , : , :
5	instantiation	41, 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	44, 25, 49, 12	, , , , , , ⊢
	: , : , :
9	assumption		⊢
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
11	instantiation	13	⊢
	: , : , : , : , :
12	instantiation	35, 14, 15	, , , , , , ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
14	instantiation	38, 16, 25, 49, 17	, , , , , , ⊢
	: , : , : , :
15	instantiation	41, 18, 19	⊢
	: , : , :
16	assumption		⊢
17	instantiation	44, 25, 49, 20	, , , , , ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
19	instantiation	21	⊢
	: , : , : , :
20	instantiation	35, 22, 23	, , , , , ⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
22	instantiation	24, 25, 52, 49, 26, 27	, , , , , ⊢
	: , : , : , : , :
23	instantiation	41, 28, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
25	instantiation	54, 32	⊢
	:
26	instantiation	44, 52, 49, 30	, , , ⊢
	: , : , :
27	instantiation	31, 55, 32, 33	, , ⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
29	instantiation	34	⊢
	: , : , :
30	instantiation	35, 36, 37	, , , ⊢
	: , : , :
31	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
32	assumption		⊢
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
35	theorem		⊢
	proveit.logic.equality.sub_left_side_into
36	instantiation	38, 39, 52, 49, 40	, , , ⊢
	: , : , : , :
37	instantiation	41, 42, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
39	assumption		⊢
40	instantiation	44, 52, 49, 45	, , ⊢
	: , : , :
41	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
43	instantiation	46	⊢
	: , :
44	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
45	instantiation	47, 48, 52, 49, 50	, , ⊢
	: , : , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
48	assumption		⊢
49	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
50	instantiation	51, 52, 53	, ⊢
	: , :
51	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
52	instantiation	54, 55	⊢
	:
53	assumption		⊢
54	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
55	assumption		⊢