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