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