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, Lambda, k
from proveit.logic import Equals, Forall
from proveit.numbers import Interval, NaturalPos, one
from proveit.physics.quantum.circuits import Gate, MultiQubitElem

# build up the expression from sub-expressions
expr = Lambda(A, Forall(instance_param_or_params = [k], instance_expr = Equals(MultiQubitElem(element = Gate(operation = A, part = one), targets = Interval(k, k)), Gate(operation = A)), domain = 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())

A \mapsto \left[\forall_{k \in \mathbb{N}^+}~\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{A~\mbox{part}~1~\mbox{on}~\{k~\ldotp \ldotp~k\}} & \qw 
} \end{array} = \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{A} & \qw 
} \end{array}\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: 26 body: 2
1	ExprTuple	26
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 28 body: 7
6	ExprTuple	28
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	28, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 22 operands: 19
16	Literal
17	Literal
18	NamedExprs	element: 20 targets: 21
19	NamedExprs	operation: 26
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	NamedExprs	operation: 26 part: 27
24	Literal
25	ExprTuple	28, 28
26	Variable
27	Literal
28	Variable