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.logic import And, Forall, InSet
from proveit.numbers import Add, Interval, Natural, Neg, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = InSet(Add(sub_expr1, t), Natural)
sub_expr3 = Add(Neg(t), one)
expr = ExprTuple(Forall(instance_param_or_params = [sub_expr1], instance_expr = sub_expr2, domain = Interval(sub_expr3, zero)), And(ExprRange(sub_expr1, sub_expr2, sub_expr3, 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(\left({_{-}a} + t\right) \in \mathbb{N}\right), \left(\left(\left(-t + 1\right) + t\right) \in \mathbb{N}\right) \land  \left(\left(\left(-t + 2\right) + t\right) \in \mathbb{N}\right) \land  \ldots \land  \left(\left(0 + t\right) \in \mathbb{N}\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: 25 body: 9
8	ExprRange	lambda_map: 10 start_index: 23 end_index: 24
9	Conditional	value: 13 condition: 11
10	Lambda	parameter: 25 body: 13
11	Operation	operator: 15 operands: 14
12	ExprTuple	25
13	Operation	operator: 15 operands: 16
14	ExprTuple	25, 17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 26 operands: 22
19	Literal
20	Literal
21	ExprTuple	23, 24
22	ExprTuple	25, 32
23	Operation	operator: 26 operands: 27
24	Literal
25	Variable
26	Literal
27	ExprTuple	28, 29
28	Operation	operator: 30 operand: 32
29	Literal
30	Literal
31	ExprTuple	32
32	Variable