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Proof step 372 from proof inv-commit (previous step)

syn0 ↔ true, zh[rp] = mkznode(r, zbrar, boolvar, boolvar0, m), adr = adr3, adr0 = adr3, err1 = ESUCCESS, err1 = err, ginval = ginval0, ginval4 = ∅, gstore = gstore3, gstore0 = gstore4, gstore1 = remove-refsize0(gstore0), gstore2 = remove-refsize0(gstore0), istore = istore3, istore0 = istore4, istore1 = remove-refsize0(istore0), istore2 = remove-refsize0(istore0), maxino2 = maxino0, nx = [], pstate = unbuffered, remove-refsize0(gstore3) = gstore3, remove-refsize0(istore3) = istore3, remove-refsize0(remove-refsize0(istore0)) = remove-refsize0(istore0), remove-refsize0(remove-refsize0(gstore0)) = remove-refsize0(gstore0), dom remove-refsize0(gstore4) ∩ ginval0 = ∅, elems nx0 ∩ ginval0 = ∅, elems nx ∩ ∅ = ∅, dom gstore3 ∪ elems nx0 = dom gstore4 ∪ ginval0, dom remove-refsize0(gstore0) ∪ elems nx = dom remove-refsize0(gstore0) ∪ ∅, btree-inv(rp, adr3, istore4, istore3, zh, ri, fi), inv(gstore4 \ ginval0), inv(gstore3), inv(istore4), inv(istore3), inv(remove-refsize0(istore0)), inv(remove-refsize0(gstore0)), inv(remove-refsize0(gstore0) \ ∅), istore3 ⊑ istore4, remove-refsize0(istore0) ⊑ remove-refsize0(istore0), pstate.index? → pstate.lnum ∈ remove-refsize0(istore0), pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ remove-refsize0(gstore0), ⌊err⌋ ∨ err = ESUCCESS ⊦ dups(nx), dups(nx0), rp ≠ null ∧ boolvar0, (∃ ri, fi. btree-inv(rp, adr0, istore2, istore1, zh, ri, fi)) ∧ inv(istore2) ∧ istore1 ⊑ istore2 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 373:
zh[rp] = mkznode(r, zbrar, boolvar, boolvar0, m), remove-refsize0(istore3) = istore3, remove-refsize0(gstore3) = gstore3, elems nx0 ∩ ginval0 = ∅, dom remove-refsize0(gstore4) ∩ ginval0 = ∅, dom gstore3 ∪ elems nx0 = dom gstore4 ∪ ginval0, btree-inv(rp, adr3, istore4, istore3, zh, ri, fi), inv(remove-refsize0(istore4)), inv(istore3), inv(istore4), inv(gstore3), inv(gstore4 \ ginval0), inv(remove-refsize0(gstore4)), istore3 ⊑ istore4 ⊦ dups(nx0), ∃ ri, fi. btree-inv(rp, adr3, remove-refsize0(istore4), remove-refsize0(istore4), zh, ri, fi), rp ≠ null ∧ boolvar0

Rule argument

Additional information

Used simplifier rules: ⊦ inv(istore) → inv(remove-refsize0(istore)); (ss)% ⊦ ¬ unbuffered.index?; (s)% ⊦ ¬ unbuffered.journal?; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ ¬ dups([]); (s)% ⊦ gstore \ ∅ = gstore; (s)% ⊦ inv(istore) → istore ⊑ istore; (s)% ⊦ remove-refsize0(remove-refsize0(istore)) = remove-refsize0(istore); (s)% ⊦ remove-refsize0(remove-refsize0(gstore)) = remove-refsize0(gstore); (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)%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)% ⊦ elems [] = ∅; (s)