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