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Proof step 35 from proof inv-commit-rec-ind (previous step)

((btree(rp, r0, adr3, height, dirty, ri, nodes(istore) | as1, as1, alladrs, ok) * P))(zh0) ↔ (∃ r, zh, zbrar, dirty1, nused. (r0 = null ⊃ ¬ dirty1 ∧ P(zh0);r = r0 ∧ zh = zh0) ∧ (dirty1 → dirty) ∧ (adr3 ∈ as1 ↔ ¬ dirty1) ∧ adr3 ∈ alladrs ∧ nsize(nused, ok) ∧ unmodified(adr3, mkznode(rp, zbrar, height = 0, dirty1, nused), nodes(istore) | as1) ∧ (( r => mkznode(rp, zbrar, height = 0, dirty1, nused) * bnode(r, zbrar, 0, nused, nused, height, dirty1, ri, nodes(istore) | as1, as1 -- adr3, alladrs -- adr3) * P) )(zh)), zh0[zbrar0[n0].child] = mkznode(r3, zbrar1, boolvar2, true, m2), zh0[r0] = mkznode(r2, zbrar0, false, true, m1), adr = zbrar0[n0].adr, err = ESUCCESS, pstate = index(m3), remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval1 = ∅, as ∩ as0 = ∅, as1 ∩ as0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval1, ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore) | as1, as1, alladrs, ok) * P))(zh0), n0 < # zbrar0, n0 < m1, btree-sub-clean(r0, n0, zh0), inv(istore0), inv(istore2), inv(gstore1), inv(gstore2 \ ginval1), inv(istore), refsize-cons(istore2, as0 ∪ as), refsize-cons(istore, as0 ∪ as1), m ∈ istore, m3 ∈ istore, m ∈ istore2, r0 ∈ zh1, r0 ∈ zh0, as1 ⊆ alladrs, as1 ⊆ dom nodes(istore), as1 ∩ dom nodes(istore2) ⊆ alladrs, as0 ⊆ dom nodes(istore2), alladrs ⊆ dom nodes(istore2), as ⊆ alladrs, as ⊆ dom nodes(istore2), as1 ∩ dom nodes(istore2) ⊆ as, as1 ⊆ dom nodes(istore2), istore0 ⊑ istore, istore0 ⊑ istore2, istore2 ⊑ istore, height = 0 → as1 = ∅, height = 0 → as = ∅, ∀ height0, zh, r0, r, zbrar, boolvar, m0, adr0, adr1, istore1, istore, pstate, m, istore0, gstore0, nx, ginval, as, as0, gstore, rp, dirty, ri, alladrs, P, adr, ino, ns, err, bv. height0 < height → zh[r0] = mkznode(r, zbrar, boolvar, true, m0) ∧ adr0 = adr1 ∧ istore1 = istore ∧ pstate = index(m) ∧ remove-refsize0(istore0) = istore0 ∧ remove-refsize0(gstore0) = gstore0 ∧ elems nx ∩ ginval = ∅ ∧ as ∩ as0 = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ ((btree(rp, r0, adr1, height0, dirty, ri, nodes(istore) | as, as, alladrs, ok) * P))(zh) ∧ inv(istore0) ∧ inv(istore) ∧ inv(gstore0) ∧ inv(gstore \ ginval) ∧ refsize-cons(istore, as0 ∪ as) ∧ m ∈ istore ∧ r0 ∈ zh ∧ as0 ⊆ dom nodes(istore) ∧ alladrs ⊆ dom nodes(istore) ∧ as ⊆ alladrs ∧ as ⊆ dom nodes(istore) ∧ istore0 ⊑ istore ∧ ¬ dups(nx) ∧ ¬ adr1 ∈ as ∧ (height0 = 0 → as = ∅) → ⟪btree_commit_rec#(r0, adr, istore0, ginval, gstore, gstore0, nx, ino, ns; adr1, err, zh, istore, pstate, bv)⟫ ( istore1 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → bv) ∧ inv(istore) ∧ istore0 ⊑ istore ∧ r0 ∈ zh ∧ (err = ESUCCESS → ¬ zh[r0].dirty ∧ pstate.index?) ∧ (∃ as1, alladrs1. refsize-cons(istore, as0 ∪ as1) ∧ as1 ∩ dom nodes(istore1) ⊆ as ∧ as1 ∩ as0 = ∅ ∧ alladrs1 ⊆ alladrs ∪ as1 ∧ ((btree(rp, r0, (err = ESUCCESS ⊃ adr1;adr0), height0, err ≠ ESUCCESS, ri, nodes(istore) | as1, as1, alladrs1, ok) * P))(zh))) ⊦ ⟪btree_commit_rec#(zbrar0[n0].child, adr1, istore0, ginval1, gstore2, gstore1, nx, maxino, ginval; adr, err, zh0, istore, pstate, syn); n := n0; if err = ESUCCESS then zh0[r0].zbranches[n].adr := adr; n := n + 1⟫ ( commit-inv (n, pstate, istore2, istore0, nx, gstore2, gstore1, ginval1, syn, err, rp, r0, adr3, height, dirty, ri, istore, as, as0, alladrs, P, zh0) ∧ (zh0[r0].usedsize - n) + n0 < m1), zbrar0[n0].child = null, dups(nx), adr3 ∈ as1, adr3 ∈ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%prefix-in: ⊦ adr ∈ istore ∧ istore ⊑ istore0 → adr ∈ istore0; (forward) from specification ablock-store-inv[index-store]%prefix-at: ⊦ adr ∈ istore ∧ istore ⊑ istore0 → istore[adr] = istore0[adr]; (forward) from specification ablock-store-inv[index-store]% ⊦ adr ∈ nodes(istore) ↔ adr ∈ istore; (s)% ⊦ adr ∈ dom iast ↔ adr ∈ iast; (s)% ⊦ BRANCH_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]%sub-in: ⊦ adr ∈ as ∧ as ⊆ as0 → adr ∈ as0; (forward) from specification set-basic[node-store]%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ((r => znd * P0))(zh) → r ∈ zh; (s)%⊦ mkznode(r, zbrar, boolvar, boolvar0, m) = mkznode(r0, zbrar0, boolvar1, boolvar2, m0) ↔ r = r0 ∧ zbrar = zbrar0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2) ∧ m = m0; (ws)% ⊦ ((r => znd * P0))(zh) → (zh[r] = znd0 ↔ znd = znd0); (s)%⊦ (( btree(rp, r, adr, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → (( btree(rp, r, adr, height, true, fi, iast, as, alladrs, nstat) * P) )(zh); (s)% ⊦ ((r => znd * P))(zh) → r ≠ null; (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]% ⊦ ¬ adr ∈ as → as -- adr = as; (s)% ⊦ unmodified(adr, mkznode(rp, zbrar, bv, true, nused), iast); (s)% ⊦ nsize(nused, ok) ↔ nused < BRANCH_SIZE; (s)% ⊦ r ∈ zh → r ≠ null; (s)