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