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.nat5
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
4	assumption		⊢
5	reference	23	⊢
6	instantiation	76	⊢
	: , :
7	instantiation	57, 8, 9	, , , , , , , , ⊢
	: , : , :
8	instantiation	10, 11, 12	, , , , , , , , ⊢
	: , :
9	instantiation	66, 13, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
11	instantiation	57, 15, 16	, , , , , , , , ⊢
	: , : , :
12	instantiation	17, 74, 75	, ⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
14	instantiation	18	⊢
	: , : , : , : , : , :
15	instantiation	19, 29, 71, 20, 21	, , , , , , , , ⊢
	: , : , : , :
16	instantiation	66, 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	50, 29, 71, 24	, , , , , , , ⊢
	: , : , :
21	assumption		⊢
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
23	instantiation	25	⊢
	: , : , : , : , :
24	instantiation	57, 26, 27	, , , , , , , ⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
26	instantiation	28, 29, 74, 71, 30, 31	, , , , , , , ⊢
	: , : , : , : , :
27	instantiation	66, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
29	instantiation	77, 54	⊢
	:
30	instantiation	50, 74, 71, 34	, , , , ⊢
	: , : , :
31	instantiation	35, 78, 54, 36	, , , ⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
33	instantiation	37	⊢
	: , : , : , :
34	instantiation	57, 38, 39	, , , , ⊢
	: , : , :
35	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
36	modus ponens	40, 41	, , , ⊢
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
38	instantiation	42, 43, 74, 71, 44	, , , , ⊢
	: , : , : , :
39	instantiation	66, 45, 46	⊢
	: , : , :
40	instantiation	47, 62, 48, 49	, , ⊢
	: , : , : , : , : , :
41	assumption		⊢
42	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
43	assumption		⊢
44	instantiation	50, 74, 71, 51	, , , ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
46	instantiation	52	⊢
	: , : , :
47	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
48	instantiation	53, 78, 54	, ⊢
	: , :
49	instantiation	55, 56	⊢
	: , :
50	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
51	instantiation	57, 58, 59	, , , ⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
53	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
54	assumption		⊢
55	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
56	instantiation	60, 61, 62	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.equality.sub_left_side_into
58	instantiation	63, 64, 74, 71, 65	, , , ⊢
	: , : , : , :
59	instantiation	66, 67, 68	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
62	assumption		⊢
63	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
64	instantiation	69, 70, 71, 72	, ⊢
	: , : , :
65	instantiation	73, 74, 75	, ⊢
	: , :
66	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
67	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
68	instantiation	76	⊢
	: , :
69	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
70	assumption		⊢
71	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
72	assumption		⊢
73	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
74	instantiation	77, 78	⊢
	:
75	assumption		⊢
76	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
77	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
78	assumption		⊢