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