Expression of type Lambda

from the theory of proveit.physics.quantum.QPE

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 Lambda, Variable
from proveit.logic import NotEquals
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum.QPE import _ket_u, _s, _t
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), Add(_t, _s)))
expr = Lambda(sub_expr1, NotEquals(sub_expr2, sub_expr2))

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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array} \neq \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 15 body: 2
1	ExprTuple	15
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 5
5	Operation	operator: 6 operands: 7
6	Literal
7	NamedExprs	element: 8 targets: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	NamedExprs	state: 14 part: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	Variable
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	22, 21
19	Literal
20	ExprTuple	22, 23
21	Literal
22	Literal
23	Literal