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Proof step 80 from proof rem-stays-reachable-aux2 (previous step)

(r1 ' + y0).last = (r ' + x).last, (r2 ' + x0).last = (r ' + x).last, x1 + r2 ' = (x + H[r2].nxt ') + r0 ' + y, (r ' + x).last ∈ H, path(r2 ' + x0, H), r2 ∈ H, H[r2].nxt ∈ H, path(r ' + x1 + r2 ', H), path(r ' + x + H[r2].nxt ', H), path(r ' + (x1 + r2 ') + r1 ' + y0, H), r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y ⊦ r1 = r2, r = r1, r2 = r, H[r2].nxt = null, dups(y0), dups(x1), dups(x1 + y0), r2 ∈ y0, r2 ∈ x1, r1 ∈ y0, r1 ∈ x1, r ∈ y0, dups(x0), r2 ∈ x0, r2 ∈ x, r ∈ x1

User applied rule cut formula

And closed the goal!

Rule argument

fma: path(r2 ' + r1 ' + y0, H)

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%path-postfix: ⊦ path(x + r ' + y, H) → (¬ path(r ' + y, H) ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%neq-03: ⊦ ¬ r ∈ x ∧ r ≠ r0 → x + r0 ' ≠ x0 + r ' + x1; from specification list[reflist] Used formulas: path(r2 ' + r1 ' + y0, H)