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, t
from proveit.numbers import Interval, Mod, Mult, Round, one
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import phase, two_pow_t
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mod(Round(Mult(two_pow_t, phase)), two_pow_t), t), part = sub_expr1), targets = Interval(one, t)))

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 \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 12 body: 2
1	ExprTuple	12
2	Operation	operator: 3 operands: 4
3	Literal
4	NamedExprs	element: 5 targets: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	NamedExprs	state: 11 part: 12
9	Literal
10	ExprTuple	13, 30
11	Operation	operator: 14 operands: 15
12	Variable
13	Literal
14	Literal
15	ExprTuple	16, 30
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 25
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operands: 28
26	Variable
27	Literal
28	ExprTuple	29, 30
29	Literal
30	Variable