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