[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 125 from proof inv-format (previous step)

pstate = index(n0), inv((∅)[n0, indexblock([], [], 0)]), inv((∅)[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)]), inv ((∅ )[n0, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ]), indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize ≤ LEB_SIZE ⊦ [apersistence_sync# (adr1, (∅)[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)] [index(n0).lnum, (∅ )[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0) ] [index(n0).lnum ] .ref-size:= indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize ], ∅, ∅, ∅, ∅, [], maxino4, ∅ ; pstate, syn ; err)] ( ¬ pstate.journal? ∧ ( pstate.index? → pstate.lnum ∈ (∅ )[n0, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ]) ∧ (pstate = unbuffered → syn) → ⟪nx := []; maxino1 := maxino4; istore0 := ∅; istore := (∅)[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)] [index(n0).lnum, (∅ )[n0, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0) ] [index(n0).lnum ] .ref-size:= indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize ]; gstore0 := ∅; gstore := ∅; ginval0 := ∅; ginval := ∅; if err = ESUCCESS then let ns = ∅ in apersistence_commit# (@(index(n0).lnum, maxino2, 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 call right

And obtained the following new goals

Proof step 126:
adr = adr1, ginval = ∅, ginval0 = ∅, gstore = ∅, gstore0 = ∅, istore = ∅, istore0 = (∅)[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)] [index(n0).lnum, (∅ )[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0) ] [index(n0).lnum ] .ref-size:= indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize ], maxino = maxino4, nx = [], pstate = index(n0), inv ((∅ )[n0, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ]), inv((∅)[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)]), inv((∅)[n0, indexblock([], [], 0)]), index(n0).lnum ∈ (∅)[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)], indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize ≤ LEB_SIZE, index(n0).index? ∨ index(n0).journal? ⊦ [if pstate = readonly then err := EROFS else if pstate = unbuffered then err := ESUCCESS else {fail_or_success#(; ; err); syn := err = ESUCCESS; skip or pstate := readonly}] ( ¬ pstate.journal? ∧ ( pstate.index? → pstate.lnum ∈ (∅ )[n0, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ]) ∧ (pstate = unbuffered → syn) → ⟪nx := []; maxino1 := maxino4; istore0 := ∅; istore := (∅)[n0, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)] [index(n0).lnum, (∅ )[n0, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino2, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0) ] [index(n0).lnum ] .ref-size:= indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize ]; gstore0 := ∅; gstore := ∅; ginval0 := ∅; ginval := ∅; if err = ESUCCESS then let ns = ∅ in apersistence_commit# (@(index(n0).lnum, maxino2, 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 = ∅)))

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_sync# (ROOTADR, ISTORE, ISTORE0, GINVAL, GSTORE, GSTORE0, NL, MAXINO, OS ; PSTATE, PSYNCED ; ERR ) {if PSTATE = readonly then ERR := EROFS else if PSTATE = unbuffered then ERR := ESUCCESS else {fail_or_success#(; ; ERR); PSYNCED := ERR = ESUCCESS; skip or PSTATE := readonly} };