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Proof step 4 from proof reachable-n-trans (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
reachable-n(H, n0, r0, r1), reachable-n(H, n1, H[r].nxt, r0), H[r].nxt ∈ H, r ∈ H, ∀ H, n0, r0, r1, r. reachable-n(H, n0, r0, r1) ∧ reachable-n(H, n1, r, r0) → reachable-n(H, n1 + n0, r, r1) ⊦ H[r].nxt = null, r = null, ∃ r2. reachable-1(H, r, r2) ∧ reachable-n(H, n1 + n0, r2, r1)

Rule argument

Additional information

Used simplifier rules: reachable-n-rec: ⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, n, r1, r0));%reachable-1-def: ⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0;%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)