Expression of type Conditional

from the theory of proveit.physics.quantum.algebra

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Conditional, X, Y
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import And, InSet
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Conditional(InSet(Qmult(A, B), LinMap(Hspace, Y)), And(InSet(Qmult(A), LinMap(X, Y)), InSet(Qmult(B), LinMap(Hspace, X))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\left(A \thinspace B\right) \in \mathcal{L}\left(\mathcal{H}, Y\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(X, Y\right) ,  \left[B\right] \in \mathcal{L}\left(\mathcal{H}, X\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 13 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 21 operands: 10
7	Operation	operator: 23 operands: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	25, 27
11	ExprTuple	28, 26
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 21 operand: 25
16	Operation	operator: 23 operands: 20
17	Operation	operator: 21 operand: 27
18	Operation	operator: 23 operands: 24
19	ExprTuple	25
20	ExprTuple	29, 26
21	Literal
22	ExprTuple	27
23	Literal
24	ExprTuple	28, 29
25	Variable
26	Variable
27	Variable
28	Variable
29	Variable