Expression of type Conditional

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, S, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet, SubsetEq
from proveit.numbers import Min, Natural, Real

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Min(a_1_to_n), S), domain = S), domain = Natural), 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\{\forall_{n \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{n} \in S}~\left({\rm Min}\left(a_{1}, a_{2}, \ldots, a_{n}\right) \in S\right)\right] \textrm{ if } S \subseteq \mathbb{R}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 12 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	36, 7
6	Lambda	parameter: 32 body: 9
7	Literal
8	ExprTuple	32
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operand: 15
11	Operation	operator: 33 operands: 14
12	Literal
13	ExprTuple	15
14	ExprTuple	32, 16
15	Lambda	parameters: 26 body: 17
16	Literal
17	Conditional	value: 18 condition: 19
18	Operation	operator: 33 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	23, 36
21	Literal
22	ExprTuple	24
23	Operation	operator: 25 operands: 26
24	ExprRange	lambda_map: 27 start_index: 31 end_index: 32
25	Literal
26	ExprTuple	28
27	Lambda	parameter: 39 body: 29
28	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
29	Operation	operator: 33 operands: 34
30	Lambda	parameter: 39 body: 35
31	Literal
32	Variable
33	Literal
34	ExprTuple	35, 36
35	IndexedVar	variable: 37 index: 39
36	Variable
37	Variable
38	ExprTuple	39
39	Variable