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 Conditional, Lambda, Variable, t
from proveit.linear_algebra import MatrixExp, Unitary
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, Neg, one, two, zero
from proveit.physics.quantum.QPE import _U, _s

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, Conditional(InSet(MatrixExp(_U, Exp(two, Neg(sub_expr1))), Unitary(Exp(two, _s))), InSet(sub_expr1, Interval(Add(Neg(t), one), zero))))

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\{U^{2^{-{_{-}a}}} \in \textrm{U}\left(2^{s}\right) \textrm{ if } {_{-}a} \in \{-t + 1~\ldotp \ldotp~0\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 34 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	34, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operand: 18
9	Operation	operator: 14 operands: 15
10	Literal
11	ExprTuple	16, 17
12	Literal
13	ExprTuple	18
14	Literal
15	ExprTuple	19, 20
16	Literal
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	ExprTuple	27, 26
22	Literal
23	ExprTuple	27, 28
24	Literal
25	ExprTuple	29, 30
26	Operation	operator: 32 operand: 34
27	Literal
28	Literal
29	Operation	operator: 32 operand: 35
30	Literal
31	ExprTuple	34
32	Literal
33	ExprTuple	35
34	Variable
35	Variable