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Proof step 3 from proof btree-repl-dirty-address (previous step)

((btree(rp, r, adr0, height, true, ri, iast, as, alladrs, nstat) * P))(zh), zh[r].dirty, r ∈ zh, as ⊆ dom iast, as ⊆ alladrs ⊦ ((btree(rp, r, adr1, height, true, ri, iast, as, (alladrs -- adr0) ++ adr1, nstat) * P))(zh), adr1 ∈ alladrs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
zh[r] = mkznode(r0, zbrar, boolvar, boolvar0, m), boolvar0, ((btree(rp, r, adr0, height, true, ri, iast, as, alladrs, nstat) * P))(zh), r ∈ zh, as ⊆ alladrs, as ⊆ dom iast ⊦ ((btree(rp, r, adr1, height, true, ri, iast, as, (alladrs -- adr0) ++ adr1, nstat) * P))(zh), adr1 ∈ alladrs

Rule argument

spec: znode name: elim seq: ⊦ ( ( (r = znd.parent ∧ zbrar = znd.zbranches) ∧ (boolvar ↔ znd.leaf)) ∧ (boolvar0 ↔ znd.dirty)) ∧ m = znd.usedsize ↔ znd = mkznode(r, zbrar, boolvar, boolvar0, m) subst: [znd, r, zbrar, boolvar, boolvar0, m] → [zh[r], r0, zbrar, boolvar, boolvar0, m]

Additional information

Used simplifier rules: ⊦ ( ( (r = znd.parent ∧ zbrar = znd.zbranches) ∧ (boolvar ↔ znd.leaf)) ∧ (boolvar0 ↔ znd.dirty)) ∧ m = znd.usedsize ↔ znd = mkznode(r, zbrar, boolvar, boolvar0, m); (elim) Used terms: zh[r], r0, zbrar, boolvar, boolvar0, m