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, 7	, , , , , , , , , ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
4	assumption		⊢
5	reference	33	⊢
6	instantiation	57	⊢
	: , : , :
7	instantiation	51, 8, 9	, , , , , , , , ⊢
	: , : , :
8	instantiation	10, 11, 12	, , , , , , , , ⊢
	: , :
9	instantiation	64, 13, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
11	instantiation	51, 15, 16	, , , , , , , , ⊢
	: , : , :
12	instantiation	17, 55, 56	, ⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
14	instantiation	18	⊢
	: , : , : , : , : , :
15	instantiation	19, 29, 74, 20, 21	, , , , , , , , ⊢
	: , : , : , :
16	instantiation	64, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
20	instantiation	34, 29, 74, 24	, , , , , , , ⊢
	: , : , :
21	assumption		⊢
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
23	instantiation	25	⊢
	: , : , : , : , :
24	instantiation	51, 26, 27	, , , , , , , ⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
26	instantiation	28, 29, 55, 74, 30, 31	, , , , , , , ⊢
	: , : , : , : , :
27	instantiation	64, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
29	instantiation	67, 59	⊢
	:
30	instantiation	34, 55, 74, 35	, , , , ⊢
	: , : , :
31	instantiation	36, 68, 59, 37	, , , ⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
33	instantiation	38	⊢
	: , : , : , :
34	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
35	instantiation	51, 39, 40	, , , , ⊢
	: , : , :
36	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
37	modus ponens	41, 42	, , , ⊢
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
39	instantiation	43, 44, 55, 74, 45	, , , , ⊢
	: , : , : , :
40	instantiation	64, 46, 47	⊢
	: , : , :
41	instantiation	48, 71, 49, 50	, , ⊢
	: , : , : , : , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
44	instantiation	51, 52, 53	, , ⊢
	: , : , :
45	instantiation	54, 55, 56	, ⊢
	: , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
47	instantiation	57	⊢
	: , : , :
48	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
49	instantiation	58, 68, 59	, ⊢
	: , :
50	instantiation	60, 61	⊢
	: , :
51	theorem		⊢
	proveit.logic.equality.sub_left_side_into
52	instantiation	72, 62, 74, 63	, , ⊢
	: , : , :
53	instantiation	64, 65, 66	⊢
	: , : , :
54	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
55	instantiation	67, 68	⊢
	:
56	assumption		⊢
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
58	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
59	assumption		⊢
60	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
61	instantiation	69, 70, 71	⊢
	: , : , :
62	instantiation	72, 73, 74, 75	, ⊢
	: , : , :
63	assumption		⊢
64	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
66	instantiation	76	⊢
	: , :
67	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
68	assumption		⊢
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
71	assumption		⊢
72	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
73	assumption		⊢
74	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
75	assumption		⊢
76	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq