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	, , , , , , ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_disassociation
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
3	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
4	reference	37	⊢
5	instantiation	47	⊢
	: , :
6	instantiation	27, 7, 8	, , , , , , ⊢
	: , : , :
7	instantiation	9, 10, 11	, , , , , , ⊢
	: , :
8	instantiation	35, 12, 13	⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_right_closure
10	assumption		⊢
11	instantiation	14, 15	, , , , , ⊢
	:
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
13	instantiation	16	⊢
	: , : , : , :
14	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
15	instantiation	27, 17, 18	, , , , , ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
17	instantiation	19, 32, 33, 20, 21	, , , , , ⊢
	: , : , : , :
18	instantiation	35, 22, 23	⊢
	: , : , :
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
20	instantiation	24, 32, 33, 25	, , , , ⊢
	: , : , :
21	assumption		⊢
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
23	instantiation	26	⊢
	: , : , :
24	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
25	instantiation	27, 28, 29	, , , , ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
27	theorem		⊢
	proveit.logic.equality.sub_left_side_into
28	instantiation	30, 31, 32, 33, 34	, , , , ⊢
	: , : , : , :
29	instantiation	35, 36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
31	instantiation	38, 39, 40, 41	, ⊢
	: , : , :
32	instantiation	42, 45	⊢
	:
33	instantiation	42, 44	⊢
	:
34	instantiation	43, 44, 45, 46	, , ⊢
	: , : , :
35	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
37	instantiation	47	⊢
	: , :
38	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
39	assumption		⊢
40	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
41	assumption		⊢
42	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
43	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
44	assumption		⊢
45	assumption		⊢
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq