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