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