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, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Min, NaturalPos, Real

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [a_1_to_m, b], instance_expr = Equals(Min(a_1_to_m, b), Min(Min(a_1_to_m), b)), domain = Real), InSet(m, NaturalPos))))

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(m \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b \in \mathbb{R}}~\left({\rm Min}\left(a_{1}, a_{2}, \ldots, a_{m}, b\right) = {\rm Min}\left({\rm Min}\left(a_{1}, a_{2}, \ldots, a_{m}\right), b\right)\right) \textrm{ if } m \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	parameter: 37 body: 3
2	ExprTuple	37
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 31 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	37, 10
9	Lambda	parameters: 22 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 29 operands: 22
19	Operation	operator: 29 operands: 23
20	ExprRange	lambda_map: 24 start_index: 36 end_index: 37
21	Operation	operator: 31 operands: 25
22	ExprTuple	33, 28
23	ExprTuple	26, 28
24	Lambda	parameter: 41 body: 27
25	ExprTuple	28, 34
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Variable
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	38, 34
33	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
34	Literal
35	Lambda	parameter: 41 body: 38
36	Literal
37	Variable
38	IndexedVar	variable: 39 index: 41
39	Variable
40	ExprTuple	41
41	Variable