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 A, B, Conditional, Lambda, S, k
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Forall(instance_param_or_params = [A, B, S], instance_expr = Equals(Equals(MultiQubitElem(element = Output(state = A, part = k), targets = S), MultiQubitElem(element = Output(state = B, part = k), targets = S)), Equals(A, B))), 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\{\forall_{A, B, S}~\left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{A~\mbox{part}~k~\mbox{on}~S} 
} \end{array} = \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{B~\mbox{part}~k~\mbox{on}~S} 
} \end{array}\right) = \left(A = B\right)\right) \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: 32 body: 2
1	ExprTuple	32
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	32, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	30, 31, 26
12	Operation	operator: 17 operands: 13
13	ExprTuple	14, 15
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	30, 31
19	Operation	operator: 22 operands: 21
20	Operation	operator: 22 operands: 23
21	NamedExprs	element: 24 targets: 26
22	Literal
23	NamedExprs	element: 25 targets: 26
24	Operation	operator: 28 operands: 27
25	Operation	operator: 28 operands: 29
26	Variable
27	NamedExprs	state: 30 part: 32
28	Literal
29	NamedExprs	state: 31 part: 32
30	Variable
31	Variable
32	Variable