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 Hspace, LinMap
from proveit.logic import Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain, var_ket_psi

# build up the expression from sub-expressions
expr = Lambda(A, Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = InClass(Qmult(A, var_ket_psi), QmultCodomain), domain = Hspace), InSet(Qmult(A), LinMap(Hspace, X))))

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())

A \mapsto \left\{\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 27 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 20 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 28 body: 11
8	Operation	operator: 25 operand: 27
9	Operation	operator: 13 operands: 14
10	ExprTuple	28
11	Conditional	value: 15 condition: 16
12	ExprTuple	27
13	Literal
14	ExprTuple	24, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	28, 24
22	Operation	operator: 25 operands: 26
23	Literal
24	Variable
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Variable