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Proof step 2 from proof reachable-n-trans (previous step)

reachable-n(H, n, r, r0), reachable-n(H, n0, r0, r1) ⊦ reachable-n(H, n + n0, r, r1)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ H, r, r0, n0, r1. reachable-n(H, n1, r, r0) ∧ reachable-n(H, n0, r0, r1) → reachable-n(H, n1 + n0, r, r1), reachable-n(H, n1 +1, r, r0), reachable-n(H, n0, r0, r1) ⊦ reachable-n(H, n1 +1 + n0, r, r1)

Rule argument

indvar: n

Additional information

Used simplifier rules: reachable-n-base: ⊦ reachable-n(H, 0, r, r0) ↔ r = r0;%nat freely generated by 0, +1;;%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2