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Proof step 9 from proof crash-neutral-set-gblock-refsize (previous step)

remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval1 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval1, inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval1), maxino2 ∈ gstore, istore1 ⊑ istore2, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore ⊦ dups(nx), ∀ n0. (n0 ∈ crash(gstore, gstore0, ginval1, nx) ↔ n0 ∈ crash(gstore[maxino2, gstore[maxino2].ref-size:= n], gstore0, ginval1, nx)) ∧ ( n0 ∈ crash(gstore, gstore0, ginval1, nx) → crash(gstore, gstore0, ginval1, nx)[n0] = crash(gstore[maxino2, gstore[maxino2].ref-size:= n], gstore0, ginval1, nx)[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems nx ∩ ginval1 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval1, inv(gstore \ ginval1), inv(gstore0), inv(istore2), inv(istore1), maxino2 ∈ gstore, istore1 ⊑ istore2, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore2 ⊦ dups(nx), (n0 ∈ crash(gstore, gstore0, ginval1, nx) ↔ n0 ∈ crash(gstore[maxino2, gstore[maxino2].ref-size:= n], gstore0, ginval1, nx)) ∧ ( n0 ∈ crash(gstore, gstore0, ginval1, nx) → (n0 ∈ nx ∨ ¬ n0 ∈ ginval1 ⊃ groupblock(gstore[n0].gndlist, gstore[n0].ladrlist, (n0 ∈ gstore0 ⊃ gstore0[n0].ref-size;0));gstore0[n0]) = crash(gstore[maxino2, gstore[maxino2].ref-size:= n], gstore0, ginval1, nx)[n0])

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ crash(gstore, gstore0, ginval, nx) → crash(gstore, gstore0, ginval, nx)[n] = (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock (gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)) ;gstore0[n] ); (s)