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