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Proof step 169 from proof rem-stays-reachable-aux2 (previous step)

H[(r ' + x).last].nxt = H[r1].nxt, (r1 ' + x0).last = (r ' + x).last, path(r1 ' + x0, H), r1 ∈ H, path(r ' + x + H[r1].nxt ' + (r0 ' + x3) + r1 ', H), path(r ' + x, H), (r ' + x).last ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, r = H[r1].nxt, r1 = r, r1 = r0, H[r1].nxt = r0, r = r0, H[r1].nxt = null, r1 ∈ x3, H[r1].nxt ∈ x3, H[r1].nxt ∈ x, r ∈ x3, r ∈ x, dups(x0), r1 ∈ x0, r1 ∈ x, r0 ∈ x3, r0 ∈ x, dups(x + x3), dups(x), dups(x3)

User applied rule cut formula

And obtained the following new goals

Proof step 170:
path(H[r1].nxt ' + (r0 ' + x3) + r1 ', H), H[(r ' + x).last].nxt = H[r1].nxt, (r1 ' + x0).last = (r ' + x).last, path(r1 ' + x0, H), r1 ∈ H, path(r ' + x + H[r1].nxt ' + (r0 ' + x3) + r1 ', H), path(r ' + x, H), (r ' + x).last ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, r = H[r1].nxt, r1 = r, r1 = r0, H[r1].nxt = r0, r = r0, H[r1].nxt = null, r1 ∈ x3, H[r1].nxt ∈ x3, H[r1].nxt ∈ x, r ∈ x3, r ∈ x, dups(x0), r1 ∈ x0, r1 ∈ x, r0 ∈ x3, r0 ∈ x, dups(x + x3), dups(x), dups(x3)

Rule argument

fma: path(H[r1].nxt ' + (r0 ' + x3) + r1 ', H)

Additional information

Used simplifier rules: path-postfix: ⊦ path(x + r ' + y, H) → (¬ path(r ' + y, H) ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used formulas: path(H[r1].nxt ' + (r0 ' + x3) + r1 ', H)