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	, , , , , , , , ⊢
	:
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
2	instantiation	37, 3, 4	, , , , , , , , ⊢
	: , : , :
3	instantiation	5, 6, 7	, , , , , , , , ⊢
	: , :
4	instantiation	44, 8, 9	⊢
	: , : , :
5	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
6	instantiation	37, 10, 11	, , , , , , , , ⊢
	: , : , :
7	instantiation	12, 59, 60	, ⊢
	: , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
9	instantiation	13	⊢
	: , : , : , : , : , :
10	instantiation	14, 15, 54, 16	, , , , , , , , ⊢
	: , : , :
11	instantiation	44, 17, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
14	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
15	instantiation	37, 19, 20	, , , , , , , ⊢
	: , : , :
16	assumption		⊢
17	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
18	instantiation	21	⊢
	: , : , : , : , :
19	instantiation	22, 41, 54, 23, 24	, , , , , , , ⊢
	: , : , : , :
20	instantiation	44, 25, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
22	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
23	instantiation	47, 41, 54, 27	, , , , , , ⊢
	: , : , :
24	assumption		⊢
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
26	instantiation	28	⊢
	: , : , : , :
27	instantiation	37, 29, 30	, , , , , , ⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
29	instantiation	52, 31, 41, 54, 32	, , , , , , ⊢
	: , : , : , :
30	instantiation	44, 33, 34	⊢
	: , : , :
31	assumption		⊢
32	instantiation	47, 41, 54, 35	, , , , , ⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
34	instantiation	36	⊢
	: , : , :
35	instantiation	37, 38, 39	, , , , , ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
37	theorem		⊢
	proveit.logic.equality.sub_left_side_into
38	instantiation	40, 41, 59, 54, 42, 43	, , , , , ⊢
	: , : , : , : , :
39	instantiation	44, 45, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
41	instantiation	64, 67	⊢
	:
42	instantiation	47, 59, 54, 48	, , ⊢
	: , : , :
43	instantiation	49, 66, 67, 50	, , , ⊢
	: , : , :
44	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
46	instantiation	51	⊢
	: , :
47	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
48	instantiation	52, 53, 59, 54, 55	, , ⊢
	: , : , : , :
49	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
50	modus ponens	56, 57	, , , ⊢
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
52	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
53	assumption		⊢
54	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
55	instantiation	58, 59, 60	, ⊢
	: , :
56	instantiation	61, 72, 62, 63	, , ⊢
	: , : , : , : , : , :
57	assumption		⊢
58	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
59	instantiation	64, 66	⊢
	:
60	assumption		⊢
61	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
62	instantiation	65, 66, 67	, ⊢
	: , :
63	instantiation	68, 69	⊢
	: , :
64	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
65	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
66	assumption		⊢
67	assumption		⊢
68	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
69	instantiation	70, 71, 72	⊢
	: , : , :
70	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
72	assumption		⊢