logo

Expression of type Lambda

from the theory of proveit.logic.booleans.implication

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, Conditional, Lambda
from proveit.logic import And, Boolean, Implies, InSet, Not
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Implies(B, Not(A)), And(Implies(A, Not(B)), InSet(A, Boolean))))
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\{B \Rightarrow (\lnot A) \textrm{ if } A \Rightarrow (\lnot B) ,  A \in \mathbb{B}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple17, 21
2Conditionalvalue: 3
condition: 4
3Operationoperator: 12
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple21, 8
6Literal
7ExprTuple9, 10
8Operationoperator: 19
operand: 17
9Operationoperator: 12
operands: 13
10Operationoperator: 14
operands: 15
11ExprTuple17
12Literal
13ExprTuple17, 16
14Literal
15ExprTuple17, 18
16Operationoperator: 19
operand: 21
17Variable
18Literal
19Literal
20ExprTuple21
21Variable