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Proof step 4 from proof reach-n-split (previous step)

reachable-n(H, n0 + m, r, r0) ⊦ n0 = 0, ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n0, r1, r0)

User applied rule structural induction

And obtained the following new goals

Proof step 5:
reachable-n(H, n0 + m0 +1, r, r0), ∀ H, n0, r, r0. reachable-n(H, n0 + m0, r, r0) → n0 = 0 ∨ (∃ r1. reachable-n(H, m0, r, r1) ∧ reachable-n(H, n0, r1, r0)) ⊦ n0 = 0, ∃ r1. reachable-n(H, m0 +1, r, r1) ∧ reachable-n(H, n0, r1, r0)

Rule argument

indvar: m

Additional information

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