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	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
2	instantiation	22, 5, 6	, , , , , , , ⊢
	: , : , :
3	reference	39	⊢
4	assumption		⊢
5	instantiation	7, 26, 39, 8, 9	, , , , , , , ⊢
	: , : , : , :
6	instantiation	29, 10, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
8	instantiation	32, 26, 39, 12	, , , , , , ⊢
	: , : , :
9	assumption		⊢
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
11	instantiation	13	⊢
	: , : , : , :
12	instantiation	22, 14, 15	, , , , , , ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
14	instantiation	37, 16, 26, 39, 17	, , , , , , ⊢
	: , : , : , :
15	instantiation	29, 18, 19	⊢
	: , : , :
16	assumption		⊢
17	instantiation	32, 26, 39, 20	, , , , , ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
19	instantiation	21	⊢
	: , : , :
20	instantiation	22, 23, 24	, , , , , ⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
22	theorem		⊢
	proveit.logic.equality.sub_left_side_into
23	instantiation	25, 26, 44, 39, 27, 28	, , , , , ⊢
	: , : , : , : , :
24	instantiation	29, 30, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
26	instantiation	49, 52	⊢
	:
27	instantiation	32, 44, 39, 33	, , ⊢
	: , : , :
28	instantiation	34, 51, 52, 35	, , , ⊢
	: , : , :
29	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
31	instantiation	36	⊢
	: , :
32	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
33	instantiation	37, 38, 44, 39, 40	, , ⊢
	: , : , : , :
34	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
35	modus ponens	41, 42	, , , ⊢
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
38	assumption		⊢
39	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
40	instantiation	43, 44, 45	, ⊢
	: , :
41	instantiation	46, 57, 47, 48	, , ⊢
	: , : , : , : , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
44	instantiation	49, 51	⊢
	:
45	assumption		⊢
46	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
47	instantiation	50, 51, 52	, ⊢
	: , :
48	instantiation	53, 54	⊢
	: , :
49	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
50	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
51	assumption		⊢
52	assumption		⊢
53	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
54	instantiation	55, 56, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
57	assumption		⊢