Less-Than-or. <. Well-founded relation on Nat.
GHC can solve this for us!
ltProof :: LTProof Nat0 Nat4LESucc LEZero
ltProof :: LTProof Nat2 Nat4LESucc (LESucc (LESucc LEZero))
ltProof :: LTProof Nat3 Nat3......error......
:: a typeCtrl KGHC 9.10.3 · lts/ghc-9.10.x · 248f8f0 · 2026-10-05
Modulefin-0.3.2Haskell2010
Less-Than-or. <. Well-founded relation on Nat.
GHC can solve this for us!
ltProof :: LTProof Nat0 Nat4LESucc LEZero
ltProof :: LTProof Nat2 Nat4LESucc (LESucc (LESucc LEZero))
ltProof :: LTProof Nat3 Nat3......error......
An evidence n < m which is the same as (1 + n le m).
\forall n : \mathbb{N}, n < n \to \bot
\forall n\, m : \mathbb{N}, n < m \to m < n \to \bot
\forall n\, m\, p : \mathbb{N}, n < m \to m < p \to n < p