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, Composition, Conditional, X, Y
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import And, Equals, InSet
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = Qmult(A)
sub_expr2 = Qmult(B)
expr = Conditional(Equals(Qmult(A, B), Composition(sub_expr1, sub_expr2)), And(InSet(sub_expr1, LinMap(X, Y)), InSet(sub_expr2, 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) = \left(\left[A\right] \circ \left[B\right]\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 23 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	27, 29
12	Literal
13	ExprTuple	17, 19
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 23 operand: 27
18	Operation	operator: 25 operands: 22
19	Operation	operator: 23 operand: 29
20	Operation	operator: 25 operands: 26
21	ExprTuple	27
22	ExprTuple	31, 28
23	Literal
24	ExprTuple	29
25	Literal
26	ExprTuple	30, 31
27	Variable
28	Variable
29	Variable
30	Variable
31	Variable