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Proof step 5 from proof cyclic-alt-def (previous step)

reachable-n(H, n1 + m, r, r0), reachable-n(H, n1, r0, r0), reachable-n(H, m, r, r0) ⊦ n1 = 0, reachable-n(H, m + n * n1, r, r0)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ H, n1, m, r, r0. reachable-n(H, n1 + m, r, r0) ∧ reachable-n(H, n1, r0, r0) ∧ reachable-n(H, m, r, r0) → n1 = 0 ∨ reachable-n(H, m + n0 * n1, r, r0), reachable-n(H, n1 + m, r, r0), reachable-n(H, n1, r0, r0), reachable-n(H, m, r, r0) ⊦ n1 = 0, reachable-n(H, m + n0 +1 * n1, r, r0)

Rule argument

[VARWITHVARSEQSARG : n, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;], [CSIMPSEQ : ⊦ m * 0 = 0], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ 0 + m = m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])]]