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Proof step 67 from proof path-dups (previous step)

(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)

User applied rule cut formula

And obtained the following new goals

Proof step 23:
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)
Proof step 66:
(r ' + x1)[m] = (r ' + x1)[n], n < m, path(r ' + x1, H), m ≤ # x1, n < # x1 ⊦ n = 0, m = n, x1 = [], ∃ m, n, r0. m < n ∧ reachable-n(H, m, r, r0) ∧ reachable-n(H, n, r, r0)

Rule argument

[fma-arg: n = 0]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (n = 0)]]