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