Expression of type ExprTuple

from the theory of proveit.numbers.number_sets.real_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, x
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import IntervalOC, Less, LessEq, Real

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(InSet(x, IntervalOC(a, b)), And(InSet(x, Real), And(Less(a, x), LessEq(x, b)).with_total_ordering_style()))), And(InSet(a, Real), InSet(b, Real)))))

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_{x}~\left(\left(x \in \left(a,b\right]\right) = \left(\left(x \in \mathbb{R}\right) \land \left(a < x \leq b\right)\right)\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R}\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: 8
4	Operation	operator: 28 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 38 body: 12
9	Operation	operator: 26 operands: 13
10	Operation	operator: 26 operands: 14
11	ExprTuple	38
12	Operation	operator: 15 operands: 16
13	ExprTuple	37, 30
14	ExprTuple	39, 30
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 26 operands: 19
18	Operation	operator: 28 operands: 20
19	ExprTuple	38, 21
20	ExprTuple	22, 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	ExprTuple	37, 39
26	Literal
27	ExprTuple	38, 30
28	Literal
29	ExprTuple	31, 32
30	Literal
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Variable
39	Variable