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Proof step 53 from proof path-dups (previous step)

firstn(m, x1) ≠ [], (r ' + x1)[m] = x2 .last, (r ' + x1)[# x2] = x2 .last, path(r ' + x2, H), reachable-n(H, # x2, r, x2 .last), # x2 < m, # x2 < # x1, m ≤ # x1, path(r ' + x1, H) ⊦ x1 = [], x2 = [], path(r ' + firstn(m, x1), H) ∧ firstn(m, x1) .last = x2 .last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
(r ' + x1)[m] = x2 .last, (r ' + x1)[# x2] = x2 .last, path(r ' + x2, H), reachable-n(H, # x2, r, x2 .last), # x2 < m, # x2 < # x1, m ≤ # x1, path(r ' + x1, H) ⊦ x1 = [], x2 = [], path(r ' + firstn(m, x1), H) ∧ firstn(m, x1) .last = x2 .last

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ firstn(n, x0) = [] ↔ n = 0])]]