Expression of type ExprTuple

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 ExprTuple, Lambda, k
from proveit.logic import Equals, Forall
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 = ExprTuple(Lambda(var_ket_psi, Forall(instance_param_or_params = [k], instance_expr = Equals(MultiQubitElem(element = Output(state = var_ket_psi, part = one), targets = Interval(k, k)), Output(state = var_ket_psi)), 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())

\left(\lvert \psi \rangle \mapsto \left[\forall_{k \in \mathbb{N}^+}~\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}\right)\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 27 body: 3
2	ExprTuple	27
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 29 body: 8
7	ExprTuple	29
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	29, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 23 operands: 20
17	Literal
18	Literal
19	NamedExprs	element: 21 targets: 22
20	NamedExprs	state: 27
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	NamedExprs	state: 27 part: 28
25	Literal
26	ExprTuple	29, 29
27	Variable
28	Literal
29	Variable