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