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 HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = Qmult(A)
sub_expr2 = Qmult(B)
expr = Conditional(Forall(instance_param_or_params = [A, B], instance_expr = Equals(Qmult(A, B), Composition(sub_expr1, sub_expr2)), conditions = [InSet(sub_expr1, LinMap(X, Y)), InSet(sub_expr2, LinMap(Hspace, X))]), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces), InClass(Y, HilbertSpaces)))

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\{\forall_{A, B~|~\left[A\right] \in \mathcal{L}\left(X, Y\right), \left[B\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left(A \thinspace B\right) = \left(\left[A\right] \circ \left[B\right]\right)\right) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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 operand: 6
2	Operation	operator: 20 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 26 body: 10
7	Operation	operator: 13 operands: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Conditional	value: 15 condition: 16
11	ExprTuple	45, 17
12	ExprTuple	46, 17
13	Literal
14	ExprTuple	43, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 38 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	ExprTuple	42, 44
27	Literal
28	ExprTuple	32, 34
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34, 35
32	Operation	operator: 38 operand: 42
33	Operation	operator: 40 operands: 37
34	Operation	operator: 38 operand: 44
35	Operation	operator: 40 operands: 41
36	ExprTuple	42
37	ExprTuple	46, 43
38	Literal
39	ExprTuple	44
40	Literal
41	ExprTuple	45, 46
42	Variable
43	Variable
44	Variable
45	Variable
46	Variable