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