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