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