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symmetric :: forall (m :: Nat) (n :: Nat). (m :=: n) -> n :=: m #

plusR :: forall (c :: Natural) (m :: Nat) (n :: Nat). (m :=: n) -> (m + c) :=: (n + c) #

plusL :: forall (c :: Natural) (m :: Nat) (n :: Nat). (m :=: n) -> (c + m) :=: (c + n) #

plusR# :: forall (c :: Natural) (m :: Nat) (n :: Nat). (m :=:# n) -> (m + c) :=:# (n + c) #

plusL# :: forall (c :: Natural) (m :: Nat) (n :: Nat). (m :=:# n) -> (c + m) :=:# (c + n) #

lift :: forall (m :: Nat) (n :: Nat). (m :=:# n) -> m :=: n #