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