Expression of type Conditional

from the theory of proveit.numbers.number_sets.integers

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, a, b, n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Integer, Interval, LessEq

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [n], instance_expr = LessEq(a, n), domain = Interval(a, b)), And(InSet(a, Integer), InSet(b, Integer)))

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 \{a~\ldotp \ldotp~b\}}~\left(a \leq n\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 21 body: 11
8	Operation	operator: 19 operands: 12
9	Operation	operator: 19 operands: 13
10	ExprTuple	21
11	Conditional	value: 14 condition: 15
12	ExprTuple	25, 16
13	ExprTuple	26, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	25, 21
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Variable
26	Variable