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Proof step 20 from proof btree-mark-dirty (previous step)

(( r => mkznode(rp0, zbrar, false, false, height0) * bnode(r, zbrar, 0, height0, height0, height1 + 1, false, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh), nsize(height0, nstat), unmodified(adr, mkznode(rp0, zbrar, false, false, height0), iast), adr ∈ alladrs, adr ∈ iast, alladrs ⊆ dom iast, ∀ zh, r, rp0, zbrar, boolvar, height0, rp, adr, ri, iast, alladrs, nstat, P. zh[r] = mkznode(rp0, zbrar, boolvar, false, height0) ∧ ((btree(rp, r, adr, height1, false, ri, iast, alladrs, alladrs, nstat) * P))(zh) ∧ r ∈ zh ∧ adr ∈ alladrs ∧ adr ∈ iast ∧ alladrs ⊆ dom iast ∧ (height1 = 0 → alladrs = ∅ ++ adr) → # alladrs = 0 ∨ alladrs = ∅ ∨ ((btree(rp, r, adr, height1, true, ri, iast, alladrs -- adr, alladrs, nstat) * P))(zh[r, mkznode(rp0, zbrar, boolvar, true, height0)]) ⊦ # alladrs = 0, alladrs = ∅, nsize(height0, nstat) ∧ (( r => mkznode(rp0, zbrar, false, true, height0) * bnode(r, zbrar, 0, height0, height0, height1 + 1, true, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh[r, mkznode(rp0, zbrar, false, true, height0)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
(( r => mkznode(rp0, zbrar, false, false, height0) * bnode(r, zbrar, 0, height0, height0, height1 + 1, false, ri, iast, alladrs -- adr, alladrs -- adr) * P) )(zh), nsize(height0, nstat), unmodified(adr, mkznode(rp0, zbrar, false, false, height0), iast), adr ∈ iast, adr ∈ alladrs, alladrs ⊆ dom iast, ∀ zh, r, rp0, zbrar, boolvar, height0, rp, adr, ri, iast, alladrs, nstat, P. zh[r] = mkznode(rp0, zbrar, boolvar, false, height0) ∧ ((btree(rp, r, adr, height1, false, ri, iast, alladrs, alladrs, nstat) * P))(zh) ∧ r ∈ zh ∧ adr ∈ alladrs ∧ adr ∈ iast ∧ alladrs ⊆ dom iast ∧ (height1 = 0 → alladrs = ∅ ++ adr) → # alladrs = 0 ∨ alladrs = ∅ ∨ ((btree(rp, r, adr, height1, true, ri, iast, alladrs -- adr, alladrs, nstat) * P))(zh[r, mkznode(rp0, zbrar, boolvar, true, height0)]) ⊦ # alladrs = 0, alladrs = ∅, ((r =>_ * bnode(r, zbrar, 0, height0, height0, height1 + 1, true, ri, iast, alladrs -- adr, alladrs -- adr) * P))(zh)

Rule argument

Additional information

Used simplifier rules: r ∈ zh ⊦ ((r => znd * P0))(zh[r, znd0]) ↔ znd = znd0 ∧ ((r =>_ * P0))(zh); (ss)% ⊦ ((r => znd * P0))(zh) → r ∈ zh; (s)%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]