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Proof step 138 from proof rem-stays-reachable-aux2 (previous step)

H[H[r0].nxt].nxt = r0, path(r ' + (x2 + r1 ') + H[r0].nxt ', H), path(r0 ' + x + r1 ', H), path(r ' + x2 + r1 ', H), r0 ∈ H, r1 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = r0, H[r0].nxt = r1, r = H[r0].nxt, r = r1, r0 = null, r0 = r, r0 = r1, dups(x), dups(x2), H[r0].nxt ∈ x2, r0 ∈ x2, r ∈ x2, r0 ∈ x, r1 ∈ x, r1 ∈ x2

User applied rule cut formula

And obtained the following new goals

Proof step 139:
H[H[r0].nxt].nxt = r0, path(r ' + x2 + r1 ', H), path(r0 ' + x + r1 ', H), path(r ' + (x2 + r1 ') + H[r0].nxt ', H), path(r1 ' + H[r0].nxt ', H), H[r0].nxt ∈ H, r1 ∈ H, r0 ∈ H ⊦ H[r0].nxt = r1, H[r0].nxt = r0, H[r0].nxt = null, r = r1, r = H[r0].nxt, r0 = r1, r0 = r, r0 = null, dups(x2), dups(x), r1 ∈ x2, r1 ∈ x, r0 ∈ x, r ∈ x2, r0 ∈ x2, H[r0].nxt ∈ x2

Rule argument

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

Additional information

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