Expression of type Lambda

from the theory of proveit.logic.classes.membership

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 C, Conditional, Lambda, x
from proveit.logic import Boolean, InClass, InSet, NotInClass

# build up the expression from sub-expressions
expr = Lambda([x, C], Conditional(InSet(NotInClass(x, C), Boolean), InSet(InClass(x, C), 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(x, C\right) \mapsto \left\{\left(x \notin_{C} C\right) \in \mathbb{B} \textrm{ if } \left(x \underset{{\scriptscriptstyle c}}{\in} C\right) \in \mathbb{B}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 12 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 9
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 12
8	Operation	operator: 11 operands: 12
9	Literal
10	Literal
11	Literal
12	ExprTuple	13, 14
13	Variable
14	Variable