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