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Proof step 71 from proof path-dups (previous step)

(r ' + x1)[m] = (r ' + x1)[n], path(r ' + x1, H), n ≤ # x1, m ≤ # x1 ⊦ n < m, m = n, ∃ 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 70:
(r ' + x1)[m] = (r ' + x1)[n], path(r ' + x1, H), n ≤ # x1, m < n, m < # x1 ⊦ m = n, x1 = [], ∃ 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 : ⊦ m < n → m ≤ n], [CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ n ≤ n0 → m < n0], [CSIMPSEQ : ⊦ m ≠ n → (¬ m < n ↔ n < m)])]]