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, 4, 5, 6, 7	, , , , , , , , ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
4	assumption		⊢
5	reference	33	⊢
6	instantiation	53	⊢
	: , : , :
7	instantiation	47, 8, 9	, , , , , , , ⊢
	: , : , :
8	instantiation	10, 11, 12	, , , , , , , ⊢
	: , :
9	instantiation	56, 13, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
11	instantiation	47, 15, 16	, , , , , , , ⊢
	: , : , :
12	instantiation	17, 51, 52	, ⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
14	instantiation	18	⊢
	: , : , : , : , : , :
15	instantiation	19, 29, 63, 20, 21	, , , , , , , ⊢
	: , : , : , :
16	instantiation	56, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
20	instantiation	34, 29, 63, 24	, , , , , , ⊢
	: , : , :
21	assumption		⊢
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
23	instantiation	25	⊢
	: , : , : , : , :
24	instantiation	47, 26, 27	, , , , , , ⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
26	instantiation	28, 29, 51, 63, 30, 31	, , , , , , ⊢
	: , : , : , : , :
27	instantiation	56, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
29	instantiation	59, 37	⊢
	:
30	instantiation	34, 51, 63, 35	, , , , ⊢
	: , : , :
31	instantiation	36, 60, 37, 38	, , ⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
33	instantiation	39	⊢
	: , : , : , :
34	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
35	instantiation	47, 40, 41	, , , , ⊢
	: , : , :
36	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
37	assumption		⊢
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
40	instantiation	42, 43, 51, 63, 44	, , , , ⊢
	: , : , : , :
41	instantiation	56, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
43	instantiation	47, 48, 49	, , ⊢
	: , : , :
44	instantiation	50, 51, 52	, ⊢
	: , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
46	instantiation	53	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.equality.sub_left_side_into
48	instantiation	61, 54, 63, 55	, , ⊢
	: , : , :
49	instantiation	56, 57, 58	⊢
	: , : , :
50	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
51	instantiation	59, 60	⊢
	:
52	assumption		⊢
53	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
54	instantiation	61, 62, 63, 64	, ⊢
	: , : , :
55	assumption		⊢
56	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
58	instantiation	65	⊢
	: , :
59	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
60	assumption		⊢
61	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
62	assumption		⊢
63	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
64	assumption		⊢
65	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq