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Proof step 39 from proof rem-stays-reachable-aux1 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
x = x1 + r ', path(H[H[r].nxt].nxt ' + x, H), path(H[H[r].nxt].nxt ' + x0 + H[r].nxt ', H), H[r].nxt ∈ H, r ∈ H ⊦ r = H[H[r].nxt].nxt, H[r].nxt = null, H[r].nxt = H[H[r].nxt].nxt, x = [], r ∈ x0, H[H[r].nxt].nxt ∈ x, dups(x)

Rule argument

spec: list-last inst: reflist name: last-elim seq: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r ' subst: [x0, r, x1] → [x, r, x1] flags: []

Additional information

Used simplifier rules: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r '; (elim) Used terms: x, r, x1