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