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