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 ExprRange, ExprTuple, Variable, t
from proveit.linear_algebra import MatrixExp, Unitary
from proveit.logic import And, Forall, 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}")
sub_expr2 = Add(Neg(t), one)
sub_expr3 = InSet(MatrixExp(_U, Exp(two, Neg(sub_expr1))), Unitary(Exp(two, _s)))
expr = ExprTuple(Forall(instance_param_or_params = [sub_expr1], instance_expr = sub_expr3, domain = Interval(sub_expr2, zero)), And(ExprRange(sub_expr1, sub_expr3, sub_expr2, 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(\forall_{{_{-}a} \in \{-t + 1~\ldotp \ldotp~0\}}~\left(U^{2^{-{_{-}a}}} \in \textrm{U}\left(2^{s}\right)\right), \left(U^{2^{-\left(-t + 1\right)}} \in \textrm{U}\left(2^{s}\right)\right) \land  \left(U^{2^{-\left(-t + 2\right)}} \in \textrm{U}\left(2^{s}\right)\right) \land  \ldots \land  \left(U^{2^{-0}} \in \textrm{U}\left(2^{s}\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Lambda	parameter: 44 body: 9
8	ExprRange	lambda_map: 10 start_index: 25 end_index: 26
9	Conditional	value: 12 condition: 11
10	Lambda	parameter: 44 body: 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	44, 16
14	Literal
15	ExprTuple	17, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operand: 29
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	Literal
31	ExprTuple	35, 36
32	ExprTuple	38, 37
33	Literal
34	ExprTuple	38, 39
35	Operation	operator: 41 operand: 43
36	Literal
37	Operation	operator: 41 operand: 44
38	Literal
39	Literal
40	ExprTuple	43
41	Literal
42	ExprTuple	44
43	Variable
44	Variable