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