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