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Proof step 14 from proof inv-recover (previous step)

adr = adr2, err = ESUCCESS, err = err0, ginval = ginval2, ginval0 = ginval3, gstore = gstore1, gstore0 = crash(gstore2, gstore1, ginval2, nx), istore = istore1, istore0 = remove-refsize0(crash(istore2, istore1)), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, btree-inv(rp, adr2, istore2, istore1, zh, ri, fi), inv(gstore2 \ ginval2), inv(gstore1), inv(istore2), inv(istore1), istore1 ⊑ istore2, pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore2, pstate1.index? → pstate1.lnum ∈ istore2, err = ESUCCESS → true ∧ inv(gstore0 \ ginval) ∧ inv(gstore) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore ∪ elems nx = dom gstore0 ∪ ginval ∧ remove-refsize0(gstore) = gstore ∧ inv(istore0) ∧ inv(istore) ∧ istore ⊑ istore0 ∧ remove-refsize0(istore) = istore ∧ (unbuffered.journal? → nx ≠ [] ∧ unbuffered.lnum = nx.last ∧ unbuffered.lnum ∈ gstore0) ∧ (unbuffered.index? → unbuffered.lnum ∈ istore0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ dups(nx), true ∧ (∃ ri, fi. btree-inv(null, adr, istore0, istore, zh0, ri, fi)) ∧ inv(gstore0 \ ginval) ∧ inv(gstore) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore ∪ elems nx = dom gstore0 ∪ ginval ∧ remove-refsize0(gstore) = gstore ∧ inv(istore0) ∧ inv(istore) ∧ istore ⊑ istore0 ∧ remove-refsize0(istore) = istore ∧ (unbuffered.journal? → nx ≠ [] ∧ unbuffered.lnum = nx.last ∧ unbuffered.lnum ∈ gstore0) ∧ (unbuffered.index? → unbuffered.lnum ∈ istore0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, btree-inv(rp, adr2, istore2, istore1, zh, ri, fi), inv(crash(gstore2, gstore1, ginval2, nx) \ ginval2), inv(gstore2 \ ginval2), inv(gstore1), inv(istore2), inv(istore1), istore1 ⊑ istore2, pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore2, pstate1.index? → pstate1.lnum ∈ istore2 ⊦ dups(nx), ∃ ri, fi. btree-inv(null, adr2, remove-refsize0(crash(istore2, istore1)), istore1, zh0, ri, fi)

Rule argument

Additional information

Used simplifier rules: ⊦ ns ⊆ ns ∪ ns0; (s)% ⊦ ns ∪ ns0 = ns0 ↔ ns ⊆ ns0; (s)%⊦ inv(gstore \ ginval) ∧ inv(gstore0) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(crash(gstore, gstore0, ginval, nx) \ ginval); (ss)%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]% ⊦ ¬ unbuffered.index?; (s)% ⊦ ¬ unbuffered.journal?; (s)%⊦ istore0 ⊑ istore ∧ istore0 = remove-refsize0(istore0) → istore0 ⊑ remove-refsize0(crash(istore, istore0)); (s)%⊦ inv(istore) ∧ istore0 ⊑ istore → inv(remove-refsize0(crash(istore, istore0))); (s)%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ dom crash(gstore, gstore0, ginval, nx) = dom gstore ∪ ginval; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)