Expression of type Conditional

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

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

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

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	29, 27
7	Operation	operator: 10 operand: 12
8	Operation	operator: 10 operand: 13
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 26 body: 14
13	Lambda	parameter: 28 body: 15
14	Conditional	value: 16 condition: 17
15	Conditional	value: 18 condition: 19
16	Operation	operator: 22 operand: 26
17	Operation	operator: 24 operands: 21
18	Operation	operator: 22 operand: 28
19	Operation	operator: 24 operands: 25
20	ExprTuple	26
21	ExprTuple	26, 27
22	Variable
23	ExprTuple	28
24	Literal
25	ExprTuple	28, 29
26	Variable
27	Variable
28	Variable
29	Variable