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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, Iff, Implies
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Iff(A, B), And(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 \Leftrightarrow B \textrm{ if } 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: 9
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 9
3Operationoperator: 5
operands: 6
4Literal
5Literal
6ExprTuple7, 8
7Operationoperator: 10
operands: 9
8Operationoperator: 10
operands: 11
9ExprTuple13, 12
10Literal
11ExprTuple12, 13
12Variable
13Variable