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