[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 59 from proof inv-commit (previous step)

syn ↔ syn0, syn1 ↔ syn, istore0[m0] = indexblock(indx, lax, m3), zh[rp] = mkznode(r, zbrar, boolvar, true, m), zh0[rp] = mkznode(r0, zbrar0, boolvar0, false, m4), adr0 = adr, adr1 = @(m0, m1, m2), err = EROFS, ginval0 = ginval4, gstore = gstore1, gstore0 = gstore2, istore = istore1, maxino = maxino0, pstate = readonly, pstate = pstate1, pstate0 = pstate, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr, istore3[n, indexblock([], [], 0)], istore1, zh, ri, fi), btree-inv(rp, adr, istore3, istore1, zh, ri, fi), btree-inv(rp, @(m0, m1, m2), istore0, istore0, zh0, ri, ri), btree-inv(rp, adr, istore0[m0, indexblock(indx, lax, m3 - m2)], istore1, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri, fi), inv(istore3[n, indexblock([], [], 0)]), inv(istore1), inv(istore3), inv(gstore1), inv(gstore2 \ ginval4), inv(istore0), rp ∈ zh, istore1 ⊑ istore0, istore1 ⊑ istore3[n, indexblock([], [], 0)], istore1 ⊑ istore3, istore3[n, indexblock([], [], 0)] ⊑ istore0, pstate1 = unbuffered → syn0, pstate1.index? → pstate1.lnum ∈ istore0, pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore2, pstate = unbuffered → syn, pstate.index? → pstate.lnum ∈ istore0, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2 ⊦ ⟪if err = ESUCCESS then apersistence_commit#(adr1, maxino1, syn1; ginval1, adr0, istore0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate0; err); if err = ESUCCESS then adr := adr1 else if true then {zh0[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (m0, adr0, istore0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate0, syn1; ; maxino); apersistence_set_iblock_refsize# (m0, maxino - m2, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate0, syn1; istore0)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore0, istore1, zh0, ri, fi)) ∧ inv(gstore2 \ ginval4) ∧ inv(gstore1) ∧ elems nx ∩ ginval4 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore0) ∧ inv(istore1) ∧ istore1 ⊑ istore0 ∧ remove-refsize0(istore1) = istore1 ∧ (pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore2) ∧ (pstate0.index? → pstate0.lnum ∈ istore0) ∧ (pstate0 = unbuffered → syn1)), dups(nx), n ∈ istore3

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 60:
syn1 ↔ syn, syn ↔ syn0, zh0[rp] = mkznode(r0, zbrar0, boolvar0, false, m4), zh[rp] = mkznode(r, zbrar, boolvar, true, m), istore0[m0] = indexblock(indx, lax, m3), adr0 = adr, adr1 = @(m0, m1, m2), err = EROFS, ginval0 = ginval4, gstore = gstore1, gstore0 = gstore2, istore = istore1, maxino = maxino0, pstate = pstate1, pstate = readonly, pstate0 = pstate, 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, adr, istore0[m0, indexblock(indx, lax, m3 - m2)], istore1, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri, fi), btree-inv(rp, @(m0, m1, m2), istore0, istore0, zh0, ri, ri), btree-inv(rp, adr, istore3, istore1, zh, ri, fi), btree-inv(rp, adr, istore3[n, indexblock([], [], 0)], istore1, zh, ri, fi), inv(istore0), inv(gstore2 \ ginval4), inv(gstore1), inv(istore3), inv(istore1), inv(istore3[n, indexblock([], [], 0)]), rp ∈ zh, istore3[n, indexblock([], [], 0)] ⊑ istore0, istore1 ⊑ istore3, istore1 ⊑ istore3[n, indexblock([], [], 0)], istore1 ⊑ istore0, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore0, pstate = unbuffered → syn, pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore2, pstate1.index? → pstate1.lnum ∈ istore0, pstate1 = unbuffered → syn0 ⊦ ⟪skip; if err = ESUCCESS then adr := adr1 else if true then {zh0[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (m0, adr0, istore0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate0, syn1; ; maxino); apersistence_set_iblock_refsize# (m0, maxino - m2, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate0, syn1; istore0)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore0, istore1, zh0, ri, fi)) ∧ inv(gstore2 \ ginval4) ∧ inv(gstore1) ∧ elems nx ∩ ginval4 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore0) ∧ inv(istore1) ∧ istore1 ⊑ istore0 ∧ remove-refsize0(istore1) = istore1 ∧ (pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore2) ∧ (pstate0.index? → pstate0.lnum ∈ istore0) ∧ (pstate0 = unbuffered → syn1)), dups(nx), n ∈ istore3

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ESUCCESS ≠ EROFS; (s)