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Proof step 4 from proof btree-repl-dirty-address (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
zh[r] = mkznode(r0, zbrar, boolvar, true, m), ((btree(rp, r, adr0, height, true, ri, iast, as, alladrs, nstat) * P))(zh), r ∈ zh, as ⊆ dom iast, as ⊆ alladrs, height = 0 → as = ∅ ⊦ ((btree(rp, r, adr1, height, true, ri, iast, as, (alladrs -- adr0) ++ adr1, nstat) * P))(zh), adr1 ∈ alladrs, adr0 ∈ as

Rule argument

Additional information

Used simplifier rules: btree-dirty-adr-notin: ⊦ r ∈ zh ∧ zh[r] = mkznode(rp0, zbrar, boolvar, true, height0) ∧ (( btree (rp, r, adr, height, dirty, ri, iast, as, alladrs, nstat) * P) )(zh) → ¬ adr ∈ as ∧ (height = 0 → as = ∅);%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]