from checker import lib, proof, props
from checker.terms import App, Const

# Prove : true == not false
p = proof.reflexivity(
    props.Eq(
        x=Const("Bool.True"),
        y=App(f=Const("Bool.not"), x=Const("Bool.False"))
    )
)
p.check()

# Prove : false == not true
p = proof.reflexivity(
    props.Eq(
        x=Const("Bool.False"),
        y=App(f=Const("Bool.not"), x=Const("Bool.True"))
    )
)
p.check()