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Proof step 74 from proof path-dups (previous step)

x = r + x1, x[m] = x[n], path(x, H), n < # x, m < # x ⊦ m = n, x = [], cyclic(r, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
(r ' + x1)[m] = (r ' + x1)[n], path(r ' + x1, H), n ≤ # x1, m ≤ # x1 ⊦ m = n, cyclic(r, H)

Rule argument

[emptyarg]

Additional information

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