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Proof step 12 from proof inv-commit-rec (previous step)

dirty0 ↔ dirty, P0 = true, zh[r0] = mkznode(r, zbrar, boolvar, true, m0), adr0 = adr1, adr1 = adr1, adr2 = adr1, adr3 = adr1, alladrs1 = alladrs, as1 = as, as2 = ∅, ginval0 = ginval, gstore1 = gstore, gstore2 = gstore0, height1 = height, ino0 = ino, istore = istore, istore1 = istore, istore2 = istore, istore3 = istore0, ns0 = ns, nx0 = nx, pstate = index(m), r1 = r0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, ri0 = ri, rp0 = null, elems nx ∩ ginval = ∅, as ∩ ∅ = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((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), zh[r0].dirty, pstate.index?, inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv-index(istore, istore0), inv-journal(nx, gstore, gstore0, ginval), inv-state(pstate, nx, gstore, istore, bv), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), refsize-cons(istore, ∅ ∪ as), m ∈ istore, adr1 ∈ istore, r0 ∈ zh, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), ∅ ⊆ dom nodes(istore), istore0 ⊑ istore, height = 0 → as = ∅ ⊦ [btree_commit_rec#(r0, adr1, istore0, ginval, gstore, gstore0, nx, ino, ns; adr1, err, zh, istore, pstate, bv)] ( istore2 ⊑ istore ∧ inv-state(pstate, nx0, gstore1, istore, bv) ∧ inv-journal(nx0, gstore1, gstore2, ginval0) ∧ inv-index(istore, istore3) ∧ r1 ∈ zh ∧ (err = ESUCCESS → ¬ zh[r1].dirty ∧ pstate.index?) ∧ (∃ as3, alladrs0. refsize-cons(istore, as2 ∪ as3) ∧ as3 ∩ dom nodes(istore2) ⊆ as1 ∧ as3 ∩ as2 = ∅ ∧ alladrs0 ⊆ alladrs1 ∪ as3 ∧ ((btree(rp0, r1, (err = ESUCCESS ⊃ adr1;adr2), height1, err ≠ ESUCCESS, ri0, nodes(istore) | as3, as3, alladrs0, ok) * P0))(zh)) → istore1 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → bv) ∧ inv(istore) ∧ istore0 ⊑ istore ∧ (err ≠ ESUCCESS → btree-inv(r0, adr0, istore, istore0, zh, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, adr1, istore, istore, zh, ri, ri) ∧ btree-inv (r0, adr0, 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)), dups(nx), adr1 ∈ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
zh[r0] = mkznode(r, zbrar, boolvar, true, m0), adr2 = adr1, istore1 = istore, pstate = index(m), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((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(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), m ∈ istore, adr1 ∈ istore, r0 ∈ zh, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), istore0 ⊑ istore, ¬ dups(nx), ¬ adr1 ∈ as, height = 0 → as = ∅ ⊦ [btree_commit_rec#(r0, adr1, 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?) ∧ (∃ 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))

Rule argument

Additional information

Used simplifier rules: ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).dirty ↔ boolvar0; (s)% ⊦ as ⊆ as; (s)% ⊦ as ⊆ dom iast → dom(iast | as) = as; (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]%btree-adrs: ⊦ (( btree (rp, rp0, adr0, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ dom iast; (forward) from specification btree-inv%⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)% ⊦ unbuffered ≠ index(m); (s)% ⊦ index(m).lnum = m; (s)% ⊦ index(m).index?; (s)% ⊦ ¬ index(m).journal?; (s)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)%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; (s)% ⊦ ∅ ⊆ 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 ∩ ∅ = ∅; (s)