Expression of type ExprTuple

from the theory of proveit.numbers.number_sets.integers

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, a, b, n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Integer, Interval, LessEq

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(Forall(instance_param_or_params = [n], instance_expr = And(LessEq(a, n), LessEq(n, b)).with_total_ordering_style(), domain = Interval(a, b)), And(InSet(a, Integer), InSet(b, Integer)))))

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(\left(a, b\right) \mapsto \left\{\forall_{n \in \{a~\ldotp \ldotp~b\}}~\left(a \leq n \leq b\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\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	parameters: 29 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 18 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 30 body: 12
9	Operation	operator: 20 operands: 13
10	Operation	operator: 20 operands: 14
11	ExprTuple	30
12	Conditional	value: 15 condition: 16
13	ExprTuple	31, 17
14	ExprTuple	32, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	30, 24
22	Operation	operator: 26 operands: 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprTuple	31, 30
26	Literal
27	ExprTuple	30, 32
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Variable
32	Variable