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spec Nat_with_< = Nat thenpred __ < __ : Nat × Nat∀i, j, k : Nat• 0 < suc(j) %{ 0< }%• ¬(i < 0) %{ <0 }%• suc(i) < suc(j) ⇔ i < j %{ s<s }%• i < s(i) %{ i<si }%• i < j ⇒ i + k < j + k %{ <⇒+<+ }%endProuver par induction sur i :∀ i, j, k : Nat, (i < j ∧ j < k ⇒ i < k)
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