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Proof step 11 from proof path-dups (previous step)

m = m0 + 1, (r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1, ¬ path(x1[m0] ' + firstn(m, x1), H) ∨ x1[m0] ≠ r ⊦ x1 = [], m = 0, reachable-n(H, m, r, r)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
m0 < # x1, path(x1[m0] ' + x1, H) ⊦ x1 = [], path(x1[m0] ' + firstn(m0 + 1, x1), H), reachable-n(H, m0 + 1, x1[m0], x1[m0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + 1 ≤ n ↔ m < n], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ (r ' + x0)[n + 1] = x0[n]])]]