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Proof step 14 from proof inv-commit-rec (previous step)

zh[r0] = mkznode(r, zbrar, boolvar, true, m0), adr2 = adr1, istore1 = istore, pstate = index(m), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((btree(null, r0, adr1, height, dirty, ri, nodes(istore) | as, as, alladrs, ok) * true))(zh), ((btree(null, null, adr1, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), ((btree(null, r0, adr1, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), refsize-cons(istore0, alladrs0), refsize-cons(istore, as), r0 ∈ zh, adr1 ∈ istore, m ∈ istore, alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, istore0 ⊑ istore, height = 0 → as = ∅ ⊦ dups(nx), adr1 ∈ as, ∀ 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?) ∧ (∃ as0, alladrs1. refsize-cons(istore, as0) ∧ as0 ∩ dom nodes(istore1) ⊆ as ∧ alladrs1 ⊆ alladrs ∪ as0 ∧ ((btree(null, r0, (err = ESUCCESS ⊃ adr1;adr2), height, err ≠ ESUCCESS, ri, nodes(istore) | as0, as0, alladrs1, ok) * true))(zh)) → (err ≠ ESUCCESS → btree-inv(r0, adr2, istore, istore0, zh, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, adr1, istore, istore, zh, ri, ri) ∧ btree-inv (r0, adr2, istore[adr1.lnum, istore[adr1.lnum].ref-size:= (istore[adr1.lnum].ref-size - adr1.size)], istore0, zh[r0, zh[r0].dirty:= true], ri, fi) ∧ ¬ zh[r0].dirty)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore[adr1] = istore2[adr1], remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((btree(null, r0, (err = ESUCCESS ⊃ adr;adr1), height, err ≠ ESUCCESS, ri, nodes(istore2) | as0, as0, alladrs1, ok) * true))(zh0), ((btree(null, r0, adr1, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh), ((btree(null, null, adr1, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), ((btree(null, r0, adr1, height, dirty, ri, nodes(istore) | as, as, alladrs, ok) * true))(zh), inv(istore2), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), refsize-cons(istore2, as0), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), adr1 ∈ istore2, r0 ∈ zh0, m ∈ istore, adr1 ∈ istore, r0 ∈ zh, m ∈ istore2, as0 ⊆ dom nodes(istore2), as0 ⊆ alladrs1, as0 ∩ dom nodes(istore) ⊆ as, alladrs1 ⊆ alladrs ∪ as0, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), as0 ∩ dom nodes(istore) ⊆ alladrs, istore ⊑ istore2, istore0 ⊑ istore2, istore0 ⊑ istore, pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore, pstate0.index? → pstate0.lnum ∈ istore2, pstate0 = unbuffered → bv, err = ESUCCESS → ¬ zh0[r0].dirty ∧ pstate0.index?, height = 0 → as = ∅ ⊦ dups(nx), adr1 ∈ as, (err ≠ ESUCCESS → btree-inv(r0, adr1, istore2, istore0, zh0, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, adr, istore2, istore2, zh0, ri, ri) ∧ btree-inv (r0, adr1, istore2[adr.lnum, istore2[adr.lnum].ref-size:= (istore2[adr.lnum].ref-size - adr.size)], istore0, zh0[r0, zh0[r0].dirty:= true], ri, fi) ∧ ¬ zh0[r0].dirty)

Rule argument

Additional information

Used simplifier rules: unc: ⊦ as ∪ as0 = as0 ∪ as; from specification set-union[node-store]%una: ⊦ (as ∪ as0) ∪ as1 = as ∪ as0 ∪ as1; from specification set-union[node-store]% ⊦ as ⊆ as ∪ as0; (s)% ⊦ as ∩ as0 ⊆ as; (s)%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]% ⊦ as ⊆ as0 ∩ as ↔ as ⊆ as0; (s)% ⊦ dom(iast | as) = dom iast ∩ as; (s)%prefix-fwd-in: ⊦ istore ⊑ istore0 ∧ n ∈ istore → n ∈ istore0; (forward) from specification ablock-store-inv[index-store]%sub-trans: ⊦ as ⊆ as0 ∧ as0 ⊆ as1 → as ⊆ as1; (forward) from specification set-basic[node-store]%btree-adrs: ⊦ (( btree (rp, rp0, adr0, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ dom iast; (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]%btree-refed-subseteq-alladrs: ⊦ (( btree(rp, r, adr, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ alladrs; (forward) from specification btree-inv%prefix-trans: ⊦ istore ⊑ istore0 ∧ istore0 ⊑ istore1 → istore ⊑ istore1; (forward) from specification ablock-store-inv[index-store]%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]