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