[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 33 from proof inv-commit (previous step)

syn0 ↔ true, zh[rp] = mkznode(r, zbrar, boolvar, true, m), adr = adr3, adr0 = adr3, err1 = err, err1 = ESUCCESS, istore = istore0[n, indexblock([], [], 0)], istore0 = istore3, istore2 = istore, pstate = index(n), pstate0 = unbuffered, remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, elems nx ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr3, istore3, istore1, zh, ri, fi), inv(gstore2 \ ginval4), inv(gstore1), inv(istore3), inv(istore1), inv(istore), rp ∈ zh, istore1 ⊑ istore3, istore1 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, ⌊err⌋ ∨ err = ESUCCESS ⊦ ⟪btree_commit_rec#(rp, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; adr, err1, zh, istore2, pstate, syn0); syn := false; if err1 = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore2, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; pstate, syn0; err1)}; if err1 = ESUCCESS then apersistence_commit#(adr, maxino1, syn0; ginval1, adr0, istore2, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate; err1); if err1 = ESUCCESS then adr3 := adr else if syn then {zh[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore2, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino - adr.size, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; istore2)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore2, istore1, zh, ri, fi)) ∧ inv(gstore2 \ ginval4) ∧ inv(gstore1) ∧ elems nx ∩ ginval4 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore2) ∧ inv(istore1) ∧ istore1 ⊑ istore2 ∧ remove-refsize0(istore1) = istore1 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn0)), dups(nx), n ∈ istore0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
zh[rp] = mkznode(r, zbrar, boolvar, true, m), adr = adr3, err1 = ESUCCESS, istore = istore3[n, indexblock([], [], 0)], pstate = index(n), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, syn0, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr3, istore3, istore1, zh, ri, fi), inv(istore3[n, indexblock([], [], 0)]), inv(istore1), inv(istore3), inv(gstore1), inv(gstore2 \ ginval4), rp ∈ zh, istore1 ⊑ istore3[n, indexblock([], [], 0)], istore1 ⊑ istore3, ¬ dups(nx), ¬ n ∈ istore3 ⊦ ⟪btree_commit_rec#(rp, adr3, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; adr, err1, zh, istore, pstate, syn0); syn := false; adr0 := adr3; if err1 = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; pstate, syn0; err1)}; if err1 = ESUCCESS then apersistence_commit#(adr, maxino1, syn0; ginval1, adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate; err1); if err1 = ESUCCESS then adr3 := adr else if syn then {zh[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino - adr.size, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; istore)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore, istore1, zh, ri, fi)) ∧ inv(gstore2 \ ginval4) ∧ inv(gstore1) ∧ elems nx ∩ ginval4 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore) ∧ inv(istore1) ∧ istore1 ⊑ istore ∧ remove-refsize0(istore1) = istore1 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn0))

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ istore[n0, iblock] ↔ n = n0 ∨ n ∈ istore; (ws)% ⊦ index(m).lnum = m; (s)% ⊦ index(m).index?; (s)% ⊦ ¬ index(m).journal?; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)