Expression of type Forall

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 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 = Forall(instance_param_or_params = [a, b, n], instance_expr = InSet(n, Interval(a, b)), domain = Integer, condition = And(LessEq(a, n), LessEq(n, b)).with_total_ordering_style())

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())

\forall_{a, b, n \in \mathbb{Z}~|~a \leq n \leq b}~\left(n \in \{a~\ldotp \ldotp~b\}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	29, 31, 30
5	Conditional	value: 6 condition: 7
6	Operation	operator: 19 operands: 8
7	Operation	operator: 21 operands: 9
8	ExprTuple	30, 10
9	ExprTuple	11, 12, 13, 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 19 operands: 17
12	Operation	operator: 19 operands: 18
13	Operation	operator: 19 operands: 20
14	Operation	operator: 21 operands: 22
15	Literal
16	ExprTuple	29, 31
17	ExprTuple	29, 23
18	ExprTuple	31, 23
19	Literal
20	ExprTuple	30, 23
21	Literal
22	ExprTuple	24, 25
23	Literal
24	Operation	operator: 27 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable