Expression of type Lambda

from the theory of proveit.physics.quantum.circuits

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 IndexedVar, Lambda, U, Variable, m
from proveit.linear_algebra import Unitary
from proveit.logic import InSet
from proveit.numbers import Exp, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, InSet(IndexedVar(U, sub_expr1), Unitary(Exp(two, m))))

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(U_{{_{-}a}} \in \textrm{U}\left(2^{m}\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: 10 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	IndexedVar	variable: 6 index: 10
5	Operation	operator: 8 operand: 11
6	Variable
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	Variable
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Literal
15	Variable