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	30, 4, 5	, , , , , , , , ⊢
	: , : , :
3	instantiation	6, 52, 53	, ⊢
	: , :
4	instantiation	7, 8, 47, 9	, , , , , , , , ⊢
	: , : , :
5	instantiation	37, 10, 11	⊢
	: , : , :
6	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
7	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
8	instantiation	30, 12, 13	, , , , , , , ⊢
	: , : , :
9	assumption		⊢
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
11	instantiation	14	⊢
	: , : , : , : , :
12	instantiation	15, 34, 47, 16, 17	, , , , , , , ⊢
	: , : , : , :
13	instantiation	37, 18, 19	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
15	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
16	instantiation	40, 34, 47, 20	, , , , , , ⊢
	: , : , :
17	assumption		⊢
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
19	instantiation	21	⊢
	: , : , : , :
20	instantiation	30, 22, 23	, , , , , , ⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
22	instantiation	45, 24, 34, 47, 25	, , , , , , ⊢
	: , : , : , :
23	instantiation	37, 26, 27	⊢
	: , : , :
24	assumption		⊢
25	instantiation	40, 34, 47, 28	, , , , , ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
27	instantiation	29	⊢
	: , : , :
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, 52, 47, 35, 36	, , , , , ⊢
	: , : , : , : , :
32	instantiation	37, 38, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
34	instantiation	57, 60	⊢
	:
35	instantiation	40, 52, 47, 41	, , ⊢
	: , : , :
36	instantiation	42, 59, 60, 43	, , , ⊢
	: , : , :
37	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	instantiation	44	⊢
	: , :
40	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
41	instantiation	45, 46, 52, 47, 48	, , ⊢
	: , : , : , :
42	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
43	modus ponens	49, 50	, , , ⊢
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
46	assumption		⊢
47	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
48	instantiation	51, 52, 53	, ⊢
	: , :
49	instantiation	54, 65, 55, 56	, , ⊢
	: , : , : , : , : , :
50	assumption		⊢
51	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
52	instantiation	57, 59	⊢
	:
53	assumption		⊢
54	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
55	instantiation	58, 59, 60	, ⊢
	: , :
56	instantiation	61, 62	⊢
	: , :
57	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
58	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
59	assumption		⊢
60	assumption		⊢
61	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
65	assumption		⊢