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Proof step 13 from proof btree-repl-dirty-address (previous step)

((r => mkznode(rp, zbrar0, false, true, nused) * bnode(r, zbrar0, 0, nused, nused, height, true, ri, iast, as, alladrs -- adr0) * P))(zh), nsize(nused, nstat), adr0 ∈ alladrs, as ⊆ alladrs, as ⊆ dom iast ⊦ # alladrs = 0, alladrs = ∅, height = 0, ((r => mkznode(rp, zbrar0, false, true, nused) * bnode(r, zbrar0, 0, nused, nused, height, true, ri, iast, as, alladrs -- adr0 -- adr1) * P))(zh), adr1 ∈ as, adr0 ∈ as, adr1 ∈ alladrs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-union, inst: node-store name: del-in seq: ⊦ ¬ adr ∈ as → as -- adr = as subst: [adr, as] → [adr1, alladrs -- adr0] flags: <all paths>

Additional information

Used simplifier rules: sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]% ⊦ adr ∈ as -- adr0 ↔ adr ≠ adr0 ∧ adr ∈ as; (s) Used terms: adr1, alladrs -- adr0