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Proof step 8 from proof inv-recovery (previous step)

adr0 = adr1, err = ESUCCESS, err = err0, ginval = ginval4, ginval0 = ginval2, ginval1 = ginval3, gstore = gstore1, gstore0 = gstore3, gstore3 = crash(gstore2, gstore1, ginval4, nx), istore = istore1, istore0 = istore3, istore3 = remove-refsize0(crash(istore2, istore1)), maxino0 = maxino1, nx0 = nx1, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems nx ∩ 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 ⊦ ⟪pstate := unbuffered, syn := true, adr0 := adr, maxino0 := maxino, nx0 := nx, ginval1 := ginval0⟫ ( err = ESUCCESS → syn ∧ 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 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore0) ∧ (pstate.index? → pstate.lnum ∈ istore0)), dups(nx)

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

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