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