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, Equals, Implies, InSet
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Equals(A, B), And(InSet(A, Boolean), InSet(B, Boolean), Implies(A, B), Implies(B, A))))
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\{A = B \textrm{ if } A \in \mathbb{B} ,  B \in \mathbb{B} ,  A \Rightarrow B ,  B \Rightarrow A\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 14
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 14
3Operationoperator: 5
operands: 6
4Literal
5Literal
6ExprTuple7, 8, 9, 10
7Operationoperator: 12
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11ExprTuple19, 17
12Literal
13ExprTuple18, 17
14ExprTuple19, 18
15Literal
16ExprTuple18, 19
17Literal
18Variable
19Variable