Expression of type Forall

from the theory of proveit.logic.sets.subtraction

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 And, Difference, Equals, Forall, InSet, NotInSet

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, A, B], instance_expr = Equals(InSet(x, Difference(A, B)), And(InSet(x, A), NotInSet(x, B))))

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_{x, A, B}~\left(\left(x \in \left(A - B\right)\right) = \left(\left(x \in A\right) \land \left(x \notin B\right)\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	23, 22, 24
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 18 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	23, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	ExprTuple	22, 24
18	Literal
19	ExprTuple	23, 22
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Variable
24	Variable