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, x
from proveit.logic import Forall, NotInSet, Or
from proveit.numbers import Integer, Interval, Less

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, x], instance_expr = NotInSet(x, Interval(a, b)), domain = Integer, condition = Or(Less(x, a), Less(b, x)))

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, x \in \mathbb{Z}~|~\left(x < a\right) \lor \left(b < x\right)}~\left(x \notin \{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	31, 32, 33
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	33, 12
10	Literal
11	ExprTuple	13, 14, 15, 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 21 operands: 19
14	Operation	operator: 21 operands: 20
15	Operation	operator: 21 operands: 22
16	Operation	operator: 23 operands: 24
17	Literal
18	ExprTuple	31, 32
19	ExprTuple	31, 25
20	ExprTuple	32, 25
21	Literal
22	ExprTuple	33, 25
23	Literal
24	ExprTuple	26, 27
25	Literal
26	Operation	operator: 29 operands: 28
27	Operation	operator: 29 operands: 30
28	ExprTuple	33, 31
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Variable
33	Variable