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, QmultCodomain, 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 = InClass(Qmult(A, var_ket_psi), QmultCodomain), 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) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\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: 26 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 16 operand: 7
3	Operation	operator: 5 operands: 6
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 39 body: 10
8	Operation	operator: 30 operands: 11
9	Operation	operator: 30 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	36, 15
12	ExprTuple	29, 15
13	Operation	operator: 16 operand: 19
14	Operation	operator: 32 operands: 18
15	Literal
16	Literal
17	ExprTuple	19
18	ExprTuple	20, 21
19	Lambda	parameter: 40 body: 23
20	Operation	operator: 37 operand: 39
21	Operation	operator: 25 operands: 26
22	ExprTuple	40
23	Conditional	value: 27 condition: 28
24	ExprTuple	39
25	Literal
26	ExprTuple	36, 29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	Variable
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	40, 36
34	Operation	operator: 37 operands: 38
35	Literal
36	Variable
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Variable