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Proof step 107 from proof inv-format (previous step)

syn0 ↔ syn, adr0 = adr1, ginval1 = ∅, ginval2 = ∅, gstore1 = ∅, gstore2 = ∅, istore = (∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)], istore1 = ∅, maxino2 = index(n).lnum, maxino3 = maxino4, n0 = indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize, nx0 = [], pstate0 = index(n), inv((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(maxino, indexnode(mkbrarray(BRANCH_SIZE), true, 0).flashsize) ', 0)]), inv((∅)[n, indexblock([], [], 0)]), inv-index(istore, ∅), inv-journal([], ∅, ∅, ∅), inv-state(index(n), [], ∅, istore, syn), index(n).lnum ∈ istore, 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)] ( inv-index(istore, istore1) ∧ inv-state(pstate0, nx0, gstore1, istore, syn0) → ⟪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 = ∅)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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