Expression of type ExprTuple

from the theory of proveit.numbers.number_sets.natural_numbers

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 Interval, Natural

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

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(n \in \mathbb{N}\right) \textrm{ if } a \in \mathbb{N} ,  b \in \mathbb{N}\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: 25 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 22 body: 13
10	Operation	operator: 19 operands: 14
11	Operation	operator: 19 operands: 15
12	ExprTuple	22
13	Conditional	value: 16 condition: 17
14	ExprTuple	26, 21
15	ExprTuple	27, 21
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	22, 21
19	Literal
20	ExprTuple	22, 23
21	Literal
22	Variable
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Variable