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 Conditional, Lambda, k
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, NaturalPos, one
from proveit.physics.quantum import var_ket_psi
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Equals(MultiQubitElem(element = Output(state = var_ket_psi, part = one), targets = Interval(k, k)), Output(state = var_ket_psi)), InSet(k, NaturalPos)))

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())

k \mapsto \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi \rangle~\mbox{part}~1~\mbox{on}~\{k~\ldotp \ldotp~k\}} 
} \end{array} = \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi \rangle} 
} \end{array} \textrm{ if } k \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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