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, Conditional, Lambda, X, Y
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Lambda([Hspace, X, Y], Conditional(Forall(instance_param_or_params = [A, B], instance_expr = InClass(Qmult(A, B), QmultCodomain), conditions = [InSet(Qmult(A), LinMap(X, Y)), InSet(Qmult(B), 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) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\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	44, 45, 42
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 21 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 27 body: 12
9	Operation	operator: 19 operands: 13
10	Operation	operator: 19 operands: 14
11	Operation	operator: 19 operands: 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	44, 18
14	ExprTuple	45, 18
15	ExprTuple	42, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 37 operands: 27
24	Literal
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	ExprTuple	41, 43
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 37 operand: 41
32	Operation	operator: 39 operands: 36
33	Operation	operator: 37 operand: 43
34	Operation	operator: 39 operands: 40
35	ExprTuple	41
36	ExprTuple	45, 42
37	Literal
38	ExprTuple	43
39	Literal
40	ExprTuple	44, 45
41	Variable
42	Variable
43	Variable
44	Variable
45	Variable