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
from proveit.numbers import Complex, Integer, Interval

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

\forall_{a, b \in \mathbb{Z}}~\left[\forall_{x \in \mathbb{C}~|~x \notin \mathbb{Z}}~\left(x \notin \{a~\ldotp \ldotp~b\}\right)\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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 25 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 19 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameter: 33 body: 13
10	Operation	operator: 26 operands: 14
11	Operation	operator: 26 operands: 15
12	ExprTuple	33
13	Conditional	value: 16 condition: 17
14	ExprTuple	30, 34
15	ExprTuple	31, 34
16	Operation	operator: 28 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	33, 21
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	33, 32
28	Literal
29	ExprTuple	33, 34
30	Variable
31	Variable
32	Literal
33	Variable
34	Literal