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Proof step 23 from proof path-dups (previous step)

n = 0, (r ' + x1)[m] = (r ' + x1)[n], n < m, path(r ' + x1, H), m ≤ # x1, n < # x1 ⊦ m = n, x1 = [], ∃ m, n, r0. m < n ∧ reachable-n(H, m, r, r0) ∧ reachable-n(H, n, r, r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
(r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1 ⊦ x1 = [], m = 0, ∃ m, n, r0. m < n ∧ reachable-n(H, m, r, r0) ∧ reachable-n(H, n, r, r0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # x0 = 0 ↔ x0 = []], [CSIMPSEQ : ⊦ 0 < m ↔ m ≠ 0], [CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ (r ' + x0)[0] = r])]]