Expression of type Lambda

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, Lambda, 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 = Lambda([Hspace, X, Y], 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(\mathcal{H}, X, Y\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	47, 48, 45
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 22 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 28 body: 12
9	Operation	operator: 15 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Conditional	value: 17 condition: 18
13	ExprTuple	47, 19
14	ExprTuple	48, 19
15	Literal
16	ExprTuple	45, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 40 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 32 operands: 31
27	Operation	operator: 32 operands: 33
28	ExprTuple	44, 46
29	Literal
30	ExprTuple	34, 36
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Operation	operator: 40 operand: 44
35	Operation	operator: 42 operands: 39
36	Operation	operator: 40 operand: 46
37	Operation	operator: 42 operands: 43
38	ExprTuple	44
39	ExprTuple	48, 45
40	Literal
41	ExprTuple	46
42	Literal
43	ExprTuple	47, 48
44	Variable
45	Variable
46	Variable
47	Variable
48	Variable