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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	9, 4, 5, 44, 6, 7, 8	, , , , , , ⊢
	: , : , : , : , :
3	instantiation	9, 10, 11, 34, 24, 12	, , , , , , ⊢
	: , : , : , : , :
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	instantiation	13	⊢
	: , : , : , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	30, 14, 15	, , , , , ⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
12	instantiation	30, 16, 17	, , , , , ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
14	instantiation	20, 49, 50, 18, 22	, , , , , ⊢
	: , : , : , :
15	instantiation	38, 23, 19	⊢
	: , : , :
16	instantiation	20, 49, 50, 21, 22	, , , , , ⊢
	: , : , : , :
17	instantiation	38, 23, 24	⊢
	: , : , :
18	instantiation	41, 49, 50, 25	, , , , ⊢
	: , : , :
19	instantiation	27	⊢
	: , : , :
20	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
21	instantiation	41, 49, 50, 26	, , , , ⊢
	: , : , :
22	assumption		⊢
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
24	instantiation	27	⊢
	: , : , :
25	instantiation	30, 28, 29	, , , , ⊢
	: , : , :
26	instantiation	30, 31, 32	, , , , ⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
28	instantiation	33, 34, 49, 50, 35	, , , , ⊢
	: , : , : , :
29	instantiation	38, 39, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.logic.equality.sub_left_side_into
31	instantiation	47, 37, 49, 50, 51	, , , , ⊢
	: , : , : , :
32	instantiation	38, 39, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
34	assumption		⊢
35	instantiation	41, 49, 50, 42	, , , ⊢
	: , : , :
36	instantiation	46	⊢
	: , :
37	instantiation	43, 44, 45, 48	, ⊢
	: , : , :
38	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	instantiation	46	⊢
	: , :
41	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
42	instantiation	47, 48, 49, 50, 51	, , , ⊢
	: , : , : , :
43	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
44	assumption		⊢
45	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
48	assumption		⊢
49	instantiation	52, 55	⊢
	:
50	instantiation	52, 54	⊢
	:
51	instantiation	53, 54, 55, 56	, , ⊢
	: , : , :
52	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
53	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
54	assumption		⊢
55	assumption		⊢
56	assumption		⊢