Expression of type Forall

from the theory of proveit.logic.sets

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 Boolean, Forall, InSet, Intersect, SubsetEq

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B], instance_expr = SubsetEq(Intersect(A, B), A), condition = Forall(instance_param_or_params = [x], instance_expr = InSet(InSet(x, B), Boolean)))

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~|~\forall_{x}~\left(\left(x \in B\right) \in \mathbb{B}\right)}~\left(\left(A \cap B\right) \subseteq A\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: 8 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 13 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operand: 11
6	Literal
7	ExprTuple	10, 16
8	Literal
9	ExprTuple	11
10	Operation	operator: 12 operands: 13
11	Lambda	parameter: 22 body: 15
12	Literal
13	ExprTuple	16, 23
14	ExprTuple	22
15	Operation	operator: 20 operands: 17
16	Variable
17	ExprTuple	18, 19
18	Operation	operator: 20 operands: 21
19	Literal
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Variable