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 S, x, y
from proveit.logic import Difference, Forall, InSet, NotEquals, Set

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [S, y], instance_expr = Forall(instance_param_or_params = [x], instance_expr = InSet(x, Difference(S, Set(y))), domain = S, condition = NotEquals(x, y)))

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_{S, y}~\left[\forall_{x \in S~|~x \neq y}~\left(x \in \left(S - \left\{y\right\}\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: 5 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	25, 29
4	Operation	operator: 5 operand: 7
5	Literal
6	ExprTuple	7
7	Lambda	parameter: 26 body: 9
8	ExprTuple	26
9	Conditional	value: 10 condition: 11
10	Operation	operator: 20 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	26, 15
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	25, 24
20	Literal
21	ExprTuple	26, 25
22	Literal
23	ExprTuple	26, 29
24	Operation	operator: 27 operand: 29
25	Variable
26	Variable
27	Literal
28	ExprTuple	29
29	Variable