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
from proveit.linear_algebra import Hspace
from proveit.logic import Equals, InSet
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
expr = Lambda(var_ket_psi, Conditional(Equals(Qmult(A, var_ket_psi), Function(Qmult(A), [var_ket_psi])), InSet(var_ket_psi, Hspace)))

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())

\lvert \psi \rangle \mapsto \left\{\left(A \thinspace \lvert \psi \rangle\right) = \left[A\right]\left(\lvert \psi \rangle\right) \textrm{ if } \lvert \psi \rangle \in \mathcal{H}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 16 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	16, 10
8	Operation	operator: 14 operands: 11
9	Operation	operator: 12 operand: 16
10	Variable
11	ExprTuple	17, 16
12	Operation	operator: 14 operand: 17
13	ExprTuple	16
14	Literal
15	ExprTuple	17
16	Variable
17	Variable