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

# build up the expression from sub-expressions
expr = Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(A, var_ket_psi), X), domain = Hspace), condition = InSet(Qmult(A), LinMap(Hspace, X))), And(InClass(Hspace, HilbertSpaces), InClass(X, 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\right) \mapsto \left\{\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \in X\right)\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \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: 27 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 17 operand: 7
3	Operation	operator: 5 operands: 6
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 38 body: 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	Conditional	value: 14 condition: 15
11	ExprTuple	35, 16
12	Literal
13	ExprTuple	34, 16
14	Operation	operator: 17 operand: 20
15	Operation	operator: 31 operands: 19
16	Literal
17	Literal
18	ExprTuple	20
19	ExprTuple	21, 22
20	Lambda	parameter: 39 body: 24
21	Operation	operator: 36 operand: 38
22	Operation	operator: 26 operands: 27
23	ExprTuple	39
24	Conditional	value: 28 condition: 29
25	ExprTuple	38
26	Literal
27	ExprTuple	35, 34
28	Operation	operator: 31 operands: 30
29	Operation	operator: 31 operands: 32
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	39, 35
33	Operation	operator: 36 operands: 37
34	Variable
35	Variable
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable