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Proof step 20 from proof inv-commit (previous step)

err0 = ESUCCESS, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval4), istore1 ⊑ istore2, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪ginval1 := ?⟫ ( inv(remove-refsize0(gstore2) \ ∅) ∧ inv(remove-refsize0(gstore2)) ∧ elems [] ∩ ∅ = ∅ ∧ ¬ dups([]) ∧ dom remove-refsize0(gstore2) ∪ elems [] = dom remove-refsize0(gstore2) ∪ ∅ ∧ remove-refsize0(remove-refsize0(gstore2)) = remove-refsize0(gstore2) ∧ inv(remove-refsize0(istore2)) ∧ inv(remove-refsize0(istore2)) ∧ remove-refsize0(istore2) ⊑ remove-refsize0(istore2) ∧ remove-refsize0(remove-refsize0(istore2)) = remove-refsize0(istore2) ∧ (unbuffered.journal? → [] ≠ [] ∧ unbuffered.lnum = [].last ∧ unbuffered.lnum ∈ remove-refsize0(gstore2)) ∧ (unbuffered.index? → unbuffered.lnum ∈ remove-refsize0(istore2))), dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, elems nx ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, inv(gstore2 \ ginval4), inv(gstore1), inv(istore2), inv(istore1), istore1 ⊑ istore2, ¬ dups(nx), pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2 ⊦ ⟪ginval1 := ?⟫ (remove-refsize0(istore2) ⊑ remove-refsize0(istore2))

Rule argument

Additional information

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