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Proof step 12 from proof rem-stays-reachable-aux2 (previous step)

H[r0].nxt = H[x.last].nxt, r0 ∈ H, r0 ∈ x, path(r ' + x, H), reachable(r, r0, H), H[r0].nxt ∈ H, x.last ∈ H ⊦ H[r0].nxt = null, reachable(r0, x.last, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + (r + x2))
Proof step 14:
H[r0].nxt = H[x.last].nxt, r0 ∈ H, ∃ x1, x2. x = x1 + (r0 + x2), path(r ' + x, H), reachable(r, r0, H), H[r0].nxt ∈ H, x.last ∈ H ⊦ H[r0].nxt = null, reachable(r0, x.last, H)

Rule argument

spec: list inst: reflist name: In seq: ⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + (r + x2)) subst: [x0, r] → [x, r0] flags: rewrite

Additional information

Used terms: x, r0