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