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