Expression of type ExprTuple

from the theory of proveit.numbers.ordering

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, S, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet, SubsetEq
from proveit.numbers import Max, NaturalPos, Real

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(S, Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Max(a_1_to_n), S), domain = S), domain = NaturalPos), SubsetEq(S, 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(S \mapsto \left\{\forall_{n \in \mathbb{N}^+}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{n} \in S}~\left({\rm Max}\left(a_{1}, a_{2}, \ldots, a_{n}\right) \in S\right)\right] \textrm{ if } S \subseteq \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	parameter: 39 body: 3
2	ExprTuple	39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 15 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	39, 10
9	Lambda	parameter: 35 body: 12
10	Literal
11	ExprTuple	35
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 18
14	Operation	operator: 36 operands: 17
15	Literal
16	ExprTuple	18
17	ExprTuple	35, 19
18	Lambda	parameters: 29 body: 20
19	Literal
20	Conditional	value: 21 condition: 22
21	Operation	operator: 36 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 39
24	Literal
25	ExprTuple	27
26	Operation	operator: 28 operands: 29
27	ExprRange	lambda_map: 30 start_index: 34 end_index: 35
28	Literal
29	ExprTuple	31
30	Lambda	parameter: 42 body: 32
31	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
32	Operation	operator: 36 operands: 37
33	Lambda	parameter: 42 body: 38
34	Literal
35	Variable
36	Literal
37	ExprTuple	38, 39
38	IndexedVar	variable: 40 index: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable