[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 105 from proof inv-format (previous step)

istore = (∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)], inv((∅)[n, indexblock([], [], 0)]), inv((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)]), indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize ≤ LEB_SIZE ⊦ ⟪apersistence_set_iblock_refsize# (index(n).lnum, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize, adr1, ∅, ∅, ∅, ∅, [], maxino4, ∅, index(n), syn; istore); pstate := index(n); nx := []; maxino1 := maxino4; istore0 := ∅; gstore0 := ∅; gstore := ∅; ginval0 := ∅; ginval := ∅; err := ESUCCESS; if err = ESUCCESS then apersistence_sync#(adr1, istore, istore0, ginval0, gstore0, gstore, nx, maxino1, ginval; pstate, syn; err); if err = ESUCCESS then let ns = ∅ in apersistence_commit# (@(index(n).lnum, maxino, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize), maxino4, syn ; ns, istore, ginval0, gstore0, adr1, istore0, gstore, nx, maxino1, ginval ; pstate, err)⟫ ( ( err = ESUCCESS → syn ∧ (∃ ri, fi. btree-inv(null, adr1, istore, istore0, zh, ri, fi)) ∧ inv(gstore0 \ ginval0) ∧ inv(gstore) ∧ elems nx ∩ ginval0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore ∪ elems nx = dom gstore0 ∪ ginval0 ∧ remove-refsize0(gstore) = gstore ∧ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore0) ∧ (pstate.index? → pstate.lnum ∈ istore)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → btree-inv(null, adr1, istore, istore0, zh, ∅, ∅) ∧ gstore0 = ∅ ∧ ginval0 = ∅ ∧ maxino1 = maxino4 ∧ nx = [] ∧ ginval = ∅))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: apersistence-asm name: inv-set-iblock-refsize seq: inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), maxino ∈ istore ⊦ ⟪apersistence_set_iblock_refsize# (maxino, n, adr, istore0, ginval, gstore, gstore0, nx, maxino0, ginval0, pstate, syn ; istore)⟫ ( inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn)) subst: [syn, pstate, ginval0, maxino0, nx, gstore0, gstore, ginval, istore0, adr, n, maxino, istore] → [syn, index(n), ∅, maxino4, [], ∅, ∅, ∅, ∅, adr1, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize, index(n).lnum, istore] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)% ⊦ ∅ \ ns = ∅; (s)% ⊦ inv(∅); (s)% ⊦ elems [] = ∅; (s)% ⊦ ns ∩ ∅ = ∅; (s)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]% ⊦ ¬ dups([]); (s)% ⊦ dom ∅ = ∅; (s)% ⊦ ns ∪ ∅ = ns; (s)%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]% ⊦ remove-refsize0(∅) = ∅; (s)%⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)% ⊦ inv(∅); (s)% ⊦ ∅ ⊑ istore; (s)% ⊦ remove-refsize0(∅) = ∅; (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)% ⊦ ¬ index(m).journal?; (s)% ⊦ index(m).index?; (s)% ⊦ index(m).lnum = m; (s)% ⊦ n ∈ istore[n, iblock]; (s)% ⊦ unbuffered ≠ index(m); (s)