Assume a language with the object constant a and the function constant s. Given r(a), ∀x.(p(x) ⇒ r(s(x))), ∀x.(q(x) ⇒ r(s(x))), and ∀x.(r(x) ⇒ p(x) ∨ q(x)), use the Fitch system with Linear Induction to prove ∀x.r(x).
I know I have to reach r(X) => r(s(X)) so I’m guessing I’ve made a mistake somewhere between steps 8 and 10, but I can’t figure it out exactly. Any help is much appreciated. Thanks. (I’m using Stanford’s proof assistant).