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Proof step 70 from proof path-dups (previous step)

(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)

User applied rule insert proof lemma

And obtained the following new goals

Proof step 69:
(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)

Rule argument

[PROOFLEMMAARG : (1, 2, 1, 1, 1, 2, 1, 1), [r, x1, m, n, H] → [r, x1, n, m, H]]

Additional information

[[CONCRETESIMPRULES : ()]]