Expression of type Conditional

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, Conditional, x
from proveit.logic import Boolean, Forall, InSet, Intersect, SubsetEq

# build up the expression from sub-expressions
expr = Conditional(SubsetEq(Intersect(A, B), A), 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())

\left\{\left(A \cap B\right) \subseteq A \textrm{ if } \forall_{x}~\left(\left(x \in B\right) \in \mathbb{B}\right)\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 operand: 8
3	Literal
4	ExprTuple	7, 13
5	Literal
6	ExprTuple	8
7	Operation	operator: 9 operands: 10
8	Lambda	parameter: 19 body: 12
9	Literal
10	ExprTuple	13, 20
11	ExprTuple	19
12	Operation	operator: 17 operands: 14
13	Variable
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Literal
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Variable