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Proof step 122 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); 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 insert program lemma

And obtained the following new goals

Rule argument

spec: apersistence-asm name: inv-sync seq: inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn) ⊦ ⟪apersistence_sync# (adr, istore, istore0, ginval, gstore, gstore0, nx, maxino, ginval0 ; pstate, syn ; err)⟫ inv-state(pstate, nx, gstore, istore, syn) subst: [ginval0, maxino, nx, gstore0, gstore, ginval, istore0, istore, adr, syn, pstate, err] → [∅, maxino4, [], ∅, ∅, ∅, ∅, (∅ )[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 ], adr1, syn, pstate, err] 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)% ⊦ index(m).lnum = m; (s)% ⊦ istore[n, iblock][n] = iblock; (s)% ⊦ indexblock(indx, lax, m).ref-size:= m0 = indexblock(indx, lax, m0); (s)% ⊦ istore[n, iblock][n, iblock0] = istore[n, iblock0]; (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)% ⊦ n ∈ istore[n, iblock]; (s)% ⊦ unbuffered ≠ index(m); (s)