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, 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 = 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\{\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..

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