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Proof step 13 from proof inv-commit-rec-ind (previous step)

syn ↔ bv, zh[r0] = mkznode(r1, zbrar, boolvar, true, m0), adr0 = adr3, adr1 = adr, adr2 = adr3, err = ESUCCESS, ginval = ns, ginval0 = ginval1, gstore = gstore1, gstore0 = gstore2, istore1 = istore, maxino = ino, n = 0, pstate = index(m), r = r0, remove-refsize0(gstore1) = gstore1, remove-refsize0(istore0) = istore0, as ∩ as0 = ∅, elems nx ∩ ginval1 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval1, ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore) | as, as, alladrs, ok) * P))(zh), inv(gstore2 \ ginval1), inv(gstore1), inv(istore), inv(istore0), refsize-cons(istore, as0 ∪ as), r0 ∈ zh, m ∈ istore, as ⊆ dom nodes(istore), as ⊆ alladrs, alladrs ⊆ dom nodes(istore), as0 ⊆ dom nodes(istore), istore0 ⊑ istore, 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))) ⊦ ⟪while n < zh[r].usedsize ∧ err = ESUCCESS do {let adr = zh[r].zbranches[n].adr, rc = zh[r].zbranches[n].child in if rc ≠ null ∧ zh[rc].dirty then {btree_commit_rec#(rc, adr1, istore0, ginval0, gstore0, gstore, nx, maxino, ginval; adr, err, zh, istore, pstate, syn); if err = ESUCCESS then zh[r].zbranches[n].adr := adr}; n := n + 1}; if err = ESUCCESS then btree_io_save#(r, adr1, istore0, ginval0, gstore0, gstore, nx, maxino, ginval; adr0, zh, istore, pstate, syn; err)⟫ ( istore1 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn) ∧ 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 ⊃ adr0;adr2), height, err ≠ ESUCCESS, ri, nodes(istore) | as1, as1, alladrs1, ok) * P))(zh))), zh[r].leaf, dups(nx), adr3 ∈ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
zh[r0] = mkznode(r1, zbrar, false, true, m0), err = ESUCCESS, gstore0 = gstore2, istore1 = istore, n = 0, pstate = index(m), r = r0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval1 = ∅, as ∩ as0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval1, ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore) | as, as, alladrs, ok) * P))(zh), inv(istore0), inv(istore), inv(gstore1), inv(gstore2 \ ginval1), 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), ¬ adr3 ∈ as, 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))) ⊦ ⟪while n < zh[r].usedsize ∧ err = ESUCCESS do {let adr = zh[r].zbranches[n].adr, rc = zh[r].zbranches[n].child in if rc ≠ null ∧ zh[rc].dirty then {btree_commit_rec#(rc, adr1, istore0, ginval1, gstore0, gstore1, nx, maxino, ginval; adr, err, zh, istore, pstate, syn); if err = ESUCCESS then zh[r].zbranches[n].adr := adr}; n := n + 1}; adr0 := adr3; if err = ESUCCESS then btree_io_save#(r, adr1, istore0, ginval1, gstore0, gstore1, nx, maxino, ginval; adr0, zh, istore, pstate, syn; err)⟫ ( istore1 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn) ∧ 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 ⊃ adr0;adr3), height, err ≠ ESUCCESS, ri, nodes(istore) | as1, as1, alladrs1, ok) * P))(zh)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).leaf ↔ boolvar; (s)%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 = ∅); (forward) from specification btree-inv%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]