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	, , , , , , ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_absorption
2	assumption		⊢
3	reference	33	⊢
4	reference	36	⊢
5	reference	18	⊢
6	instantiation	54, 7, 8	, , , , , ⊢
	: , : , :
7	instantiation	9, 10, 13	, , , , , ⊢
	: , : , :
8	instantiation	20, 11, 12, 13	, , , , , ⊢
	: , : , : , :
9	theorem		⊢
	proveit.logic.equality.sub_right_side_into
10	instantiation	54, 14, 15	, , , , , ⊢
	: , : , :
11	instantiation	16, 33, 17, 36, 18, 19	, , , , , ⊢
	: , : , : , : , : , :
12	instantiation	20, 21, 22, 23	, , , , , ⊢
	: , : , : , :
13	instantiation	24, 62, 47, 38, 39	, , , , , ⊢
	: , : , :
14	instantiation	58, 70, 71, 25, 60	, , , , , ⊢
	: , : , : , :
15	instantiation	61, 62, 26	⊢
	: , : , :
16	theorem		⊢
	proveit.physics.quantum.algebra.qmult_disassociation
17	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
18	instantiation	67	⊢
	: , :
19	instantiation	54, 27, 28	, , , , , ⊢
	: , : , :
20	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
21	instantiation	32, 29, 30, 64, 44, 31, 49	, , , , , ⊢
	: , : , : , : , :
22	instantiation	32, 33, 36, 69, 38, 34	, , , , , ⊢
	: , : , : , : , :
23	instantiation	35, 62, 36, 37, 69, 64, 38, 39	, , , , , ⊢
	: , : , : , :
24	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
25	instantiation	65, 70, 71, 40	, , , , ⊢
	: , : , :
26	instantiation	67	⊢
	: , :
27	instantiation	41, 64, 42	, , , , , ⊢
	: , :
28	instantiation	61, 43, 44	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
30	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
34	instantiation	54, 45, 46	, , , , ⊢
	: , : , :
35	theorem		⊢
	proveit.physics.quantum.algebra.qmult_scalar_association
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
37	instantiation	67	⊢
	: , :
38	instantiation	67	⊢
	: , :
39	instantiation	58, 70, 71, 72, 60	, , , ⊢
	: , : , : , :
40	instantiation	68, 47, 70, 71, 72	, , , , ⊢
	: , : , : , :
41	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_right_closure
42	instantiation	48, 49	, , , , ⊢
	:
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
44	instantiation	50	⊢
	: , : , :
45	instantiation	58, 70, 71, 51, 60	, , , , ⊢
	: , : , : , :
46	instantiation	61, 62, 52	⊢
	: , : , :
47	instantiation	53, 69, 64	, ⊢
	: , :
48	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
49	instantiation	54, 55, 56	, , , , ⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
51	instantiation	65, 70, 71, 57	, , , ⊢
	: , : , :
52	instantiation	67	⊢
	: , :
53	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
54	theorem		⊢
	proveit.logic.equality.sub_left_side_into
55	instantiation	58, 70, 71, 59, 60	, , , , ⊢
	: , : , : , :
56	instantiation	61, 62, 63	⊢
	: , : , :
57	instantiation	68, 64, 70, 71, 72	, , , ⊢
	: , : , : , :
58	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
59	instantiation	65, 70, 71, 66	, , , ⊢
	: , : , :
60	assumption		⊢
61	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
63	instantiation	67	⊢
	: , :
64	assumption		⊢
65	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
66	instantiation	68, 69, 70, 71, 72	, , , ⊢
	: , : , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
68	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
69	assumption		⊢
70	instantiation	73, 76	⊢
	:
71	instantiation	73, 75	⊢
	:
72	instantiation	74, 75, 76, 77	, , ⊢
	: , : , :
73	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
74	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
75	assumption		⊢
76	assumption		⊢
77	assumption		⊢