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