logo

Expression of type Lambda

from the theory of proveit.logic.sets.disjointness

In [1]:
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
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A, B], Iff(Disjoint(A, B), Equals(Intersect(A, B), EmptySet)))
expr:
In [3]:
# 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
In [4]:
# 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)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 12
body: 1
1Operationoperator: 2
operands: 3
2Literal
3ExprTuple4, 5
4Operationoperator: 6
operands: 12
5Operationoperator: 7
operands: 8
6Literal
7Literal
8ExprTuple9, 10
9Operationoperator: 11
operands: 12
10Literal
11Literal
12ExprTuple13, 14
13Variable
14Variable