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