Expression of type Implies

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

# build up the expression from sub-expressions
expr = Implies(Forall(instance_param_or_params = [x], instance_expr = Px, domain = A), Forall(instance_param_or_params = [y], instance_expr = Py, domain = 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())

\left[\forall_{x \in A}~P\left(x\right)\right] \Rightarrow \left[\forall_{y \in B}~P\left(y\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 22 body: 10
9	Lambda	parameter: 24 body: 11
10	Conditional	value: 12 condition: 13
11	Conditional	value: 14 condition: 15
12	Operation	operator: 18 operand: 22
13	Operation	operator: 20 operands: 17
14	Operation	operator: 18 operand: 24
15	Operation	operator: 20 operands: 21
16	ExprTuple	22
17	ExprTuple	22, 23
18	Variable
19	ExprTuple	24
20	Literal
21	ExprTuple	24, 25
22	Variable
23	Variable
24	Variable
25	Variable