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, Function, Lambda, X
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import Equals, Forall, InSet
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = Lambda(A, Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qmult(A, var_ket_psi), Function(sub_expr2, sub_expr1)), domain = Hspace), InSet(sub_expr2, 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) = \left[A\right]\left(\lvert \psi \rangle\right)\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: 28 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 17 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	23, 8
7	Lambda	parameter: 27 body: 9
8	Operation	operator: 10 operands: 11
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	21, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Variable
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	27, 21
19	Operation	operator: 25 operands: 22
20	Operation	operator: 23 operand: 27
21	Variable
22	ExprTuple	28, 27
23	Operation	operator: 25 operand: 28
24	ExprTuple	27
25	Literal
26	ExprTuple	28
27	Variable
28	Variable