Expression of type Forall

from the theory of proveit.logic.sets.inclusion

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, P, Px, Py, x, y
from proveit.logic import Exists, Forall, Implies, SubsetEq

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B, P], instance_expr = Implies(Exists(instance_param_or_params = [x], instance_expr = Px, domain = A), Exists(instance_param_or_params = [y], instance_expr = Py, domain = B)), condition = SubsetEq(A, 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_{A, B, P~|~A \subseteq B}~\left(\left[\exists_{x \in A}~P\left(x\right)\right] \Rightarrow \left[\exists_{y \in B}~P\left(y\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	32, 34, 27
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	32, 34
12	Operation	operator: 15 operand: 17
13	Operation	operator: 15 operand: 18
14	ExprTuple	17
15	Literal
16	ExprTuple	18
17	Lambda	parameter: 31 body: 19
18	Lambda	parameter: 33 body: 20
19	Conditional	value: 21 condition: 22
20	Conditional	value: 23 condition: 24
21	Operation	operator: 27 operand: 31
22	Operation	operator: 29 operands: 26
23	Operation	operator: 27 operand: 33
24	Operation	operator: 29 operands: 30
25	ExprTuple	31
26	ExprTuple	31, 32
27	Variable
28	ExprTuple	33
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Variable
33	Variable
34	Variable