Expression of type Lambda

from the theory of proveit.logic.sets.disjointness

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, Lambda
from proveit.logic import Disjoint, EmptySet, Equals, Iff, Intersect

# build up the expression from sub-expressions
expr = Lambda([A, B], Iff(Disjoint(A, B), Equals(Intersect(A, B), EmptySet)))

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(A, B\right) \mapsto \left(\textrm{disjoint}\left(A, B\right) \Leftrightarrow \left(\left(A \cap B\right) = \emptyset\right)\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	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 6 operands: 12
5	Operation	operator: 7 operands: 8
6	Literal
7	Literal
8	ExprTuple	9, 10
9	Operation	operator: 11 operands: 12
10	Literal
11	Literal
12	ExprTuple	13, 14
13	Variable
14	Variable