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