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, U, Variable, s, t
from proveit.linear_algebra import MatrixExp
from proveit.numbers import Add, Exp, Interval, Neg, one, two
from proveit.physics.quantum.circuits import Gate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, MultiQubitElem(element = Gate(operation = MatrixExp(U, Exp(two, Neg(Variable("_b", latex_format = r"{_{-}b}")))), part = sub_expr1), targets = Interval(Add(t, one), Add(t, s))))

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{
& & \gate{U^{2^{-{_{-}b}}}~\mbox{part}~{_{-}a}~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \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	operation: 11 part: 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 15 operands: 16
12	Variable
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	ExprTuple	20, 21
17	ExprTuple	23, 22
18	Literal
19	ExprTuple	23, 24
20	Variable
21	Operation	operator: 25 operands: 26
22	Literal
23	Variable
24	Variable
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Variable