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 Forall, Implies, superset_eq

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B, P], instance_expr = Implies(Forall(instance_param_or_params = [x], instance_expr = Px, domain = A), Forall(instance_param_or_params = [y], instance_expr = Py, domain = B)), condition = superset_eq(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 \supseteq B}~\left(\left[\forall_{x \in A}~P\left(x\right)\right] \Rightarrow \left[\forall_{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: 14 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	31, 33, 26
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	33, 31
11	Operation	operator: 14 operand: 16
12	Operation	operator: 14 operand: 17
13	ExprTuple	16
14	Literal
15	ExprTuple	17
16	Lambda	parameter: 30 body: 18
17	Lambda	parameter: 32 body: 19
18	Conditional	value: 20 condition: 21
19	Conditional	value: 22 condition: 23
20	Operation	operator: 26 operand: 30
21	Operation	operator: 28 operands: 25
22	Operation	operator: 26 operand: 32
23	Operation	operator: 28 operands: 29
24	ExprTuple	30
25	ExprTuple	30, 31
26	Variable
27	ExprTuple	32
28	Literal
29	ExprTuple	32, 33
30	Variable
31	Variable
32	Variable
33	Variable