Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left({_{-}a} \mapsto \left\{U^{2^{-{_{-}a}}} \in \textrm{U}\left(2^{s}\right) \textrm{ if } {_{-}a} \in \{-t + 1~\ldotp \ldotp~0\}\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: 35 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	35, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operand: 19
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19
15	Literal
16	ExprTuple	20, 21
17	Literal
18	Operation	operator: 23 operands: 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	ExprTuple	28, 27
23	Literal
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	30, 31
27	Operation	operator: 33 operand: 35
28	Literal
29	Literal
30	Operation	operator: 33 operand: 36
31	Literal
32	ExprTuple	35
33	Literal
34	ExprTuple	36
35	Variable
36	Variable