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Proof step 214 from proof inv-io-save (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, true, m0), adr = adr1, istore0 = istore3, pstate = index(m), remove-refsize0(istore2) = istore2, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, ((btree(rp, r, adr1, height, dirty, ri, nodes(istore3), as, alladrs, ok) * P))(zh), btree-sub-clean(r, m0, zh), inv(istore2), inv(istore3), inv(gstore1), inv(gstore2 \ ginval2), refsize-cons(istore3, as0 ∪ as), m ∈ istore3, r ∈ zh, n ≤ LEB_SIZE, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize ≤ n, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize ≤ LEB_SIZE, as ⊆ alladrs, alladrs ⊆ dom nodes(istore3), as0 ⊆ dom nodes(istore3), as ⊆ dom nodes(istore3), istore2 ⊑ istore3, ¬ dups(nx), ¬ adr1 ∈ as, height = 0 → as = ∅ ⊦ [apersistence_add_ind# (save(mkznode(r0, zbrar, boolvar, true, m0)), adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval; adr, istore3, pstate, syn; err)] ( inv(istore3) ∧ istore2 ⊑ istore3 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore3) ∧ (pstate = unbuffered → syn) → ⟪if err = ESUCCESS then let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore3, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, pstate, syn; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino + adr.size, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, pstate, syn; istore3)}; if err = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore3, as0 ∪ (err = ESUCCESS ⊃ as ++ adr;as)) ∧ inv(istore3) ∧ istore2 ⊑ istore3 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore3) ∧ (pstate = unbuffered → syn) ∧ istore0 ⊑ istore3 ∧ r ∈ zh ∧ (err = ESUCCESS → ¬ adr ∈ as) ∧ dom nodes(istore3) = dom nodes(istore0) ∪ (err = ESUCCESS ⊃ ∅ ++ adr;∅) ∧ (err = ESUCCESS → ¬ adr ∈ istore0) ∧ (( btree (rp, r, (err = ESUCCESS ⊃ adr;adr1), height, err ≠ ESUCCESS, ri, nodes(istore3), (err = ESUCCESS ⊃ as ++ adr;as), (err = ESUCCESS ⊃ (alladrs -- adr1) ++ adr;alladrs), ok) * P) )(zh) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → pstate.index? ∧ ¬ zh[r].dirty)))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 215:
zh[r] = mkznode(r0, zbrar, boolvar, true, m0), adr = adr1, ginval0 = ginval2, gstore = gstore1, gstore0 = gstore2, ind = save(mkznode(r0, zbrar, boolvar, true, m0)), istore = istore3, istore0 = istore2, istore1 = istore3, pstate = index(m), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore2) = istore2, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, ((btree(rp, r, adr1, height, dirty, ri, nodes(istore3), as, alladrs, ok) * P))(zh), btree-sub-clean(r, m0, zh), inv(gstore2 \ ginval2), inv(gstore1), inv(istore3), inv(istore2), refsize-cons(istore3, as0 ∪ as), r ∈ zh, m ∈ istore3, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize ≤ LEB_SIZE, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize ≤ n, n ≤ LEB_SIZE, as ⊆ dom nodes(istore3), as0 ⊆ dom nodes(istore3), alladrs ⊆ dom nodes(istore3), as ⊆ alladrs, istore2 ⊑ istore3, height = 0 → as = ∅ ⊦ [if pstate.index? ∨ pstate = readonly then if pstate = readonly then err0 := EROFS else {choose maxino, err with ¬ @(pstate.lnum, maxino, ind.flashsize) ∈ istore ∧ err = ESUCCESS ∨ ⌊err⌋ in adr := @(pstate.lnum, maxino, ind.flashsize), err0 := err; if err0 = ESUCCESS then {istore[pstate.lnum].indlist := istore[pstate.lnum].indlist + ind; istore[pstate.lnum].ladrlist := istore[pstate.lnum].ladrlist + @(adr.pos, adr.size)} else adr := ?, pstate := readonly; syn := ?} else abort] ( inv(istore) ∧ istore2 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn) → ⟪err := err0, istore3 := istore; if err = ESUCCESS then let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore3, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, pstate, syn; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino + adr.size, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino0, ginval, pstate, syn; istore3)}; if err = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore3, as0 ∪ (err = ESUCCESS ⊃ as ++ adr;as)) ∧ inv(istore3) ∧ istore2 ⊑ istore3 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore3) ∧ (pstate = unbuffered → syn) ∧ istore1 ⊑ istore3 ∧ r ∈ zh ∧ (err = ESUCCESS → ¬ adr ∈ as) ∧ dom nodes(istore3) = dom nodes(istore1) ∪ (err = ESUCCESS ⊃ ∅ ++ adr;∅) ∧ (err = ESUCCESS → ¬ adr ∈ istore1) ∧ (( btree (rp, r, (err = ESUCCESS ⊃ adr;adr1), height, err ≠ ESUCCESS, ri, nodes(istore3), (err = ESUCCESS ⊃ as ++ adr;as), (err = ESUCCESS ⊃ (alladrs -- adr1) ++ adr;alladrs), ok) * P) )(zh) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → pstate.index? ∧ ¬ zh[r].dirty))), dups(nx), adr1 ∈ as

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_add_ind# (IND, ROOTADR, ISTORE0, GINVAL, GSTORE, GSTORE0, NL, MAXINO, OS ; ADR, ISTORE, PSTATE, PSYNCED ; ERR ) {if PSTATE.index? ∨ PSTATE = readonly then if PSTATE = readonly then ERR := EROFS else {choose OFFSET, ERR0 with ¬ @(PSTATE.lnum, OFFSET, IND.flashsize) ∈ ISTORE ∧ ERR0 = ESUCCESS ∨ ⌊ERR0⌋ in ADR := @(PSTATE.lnum, OFFSET, IND.flashsize), ERR := ERR0; if ERR = ESUCCESS then {ISTORE[PSTATE.lnum].indlist := ISTORE[PSTATE.lnum].indlist + IND; ISTORE[PSTATE.lnum].ladrlist := ISTORE[PSTATE.lnum].ladrlist + @(ADR.pos, ADR.size)} else ADR := ?, PSTATE := readonly; PSYNCED := ?} else abort };