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