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Proof step 31 from proof inv-addn (previous step)

err0 = ESUCCESS ↔ # lax = # gndx, abs-log(nx0, gstore1 ↓) = abs-log(nx1, gstore2 ↓), ax = lax.to-adr(nx.last), err = err0, fi = fi1, fi0 = fi2, gstore = gstore1, jro = jro0, nodes(gstore1 ↓, jro0) = nodes(gstore2 ↓, jro1), nx = nx0, remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro1 = ∅, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro0, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(gstore1[nx0.last]), inv(gstore1 \ jro0), inv(gstore2 \ jro1), inv(gstore0), inv-flashsize(prefixn(# lax, gndx), lax), refsize-cons(gstore1, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), transaction(ndx, gndx), valid-journal-head(nx0, gstore1, jro0), nx.last ∈ gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))], nx0.last ∈ gstore1, nx.last ∈ gstore, pmaxino ≤ jmaxino1, # lax ≤ # gndx, dom gstore2 ⊆ dom gstore1, fi1.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore1, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1), ⌊err0⌋ ∨ err0 = ESUCCESS → nx.last ∈ gstore ∧ nx ≠ [], ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [if err ≠ ESUCCESS then ax := ?; jvalid := ?] ( inv ( gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))] [nx.last, gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))][nx.last] .ladrlist:= (gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))][nx.last].ladrlist + lax) ] \ jro0) ∧ dom gstore0 ∪ elems nx0 = dom gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))] [nx.last, gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))][nx.last] .ladrlist:= (gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))][nx.last].ladrlist + lax) ] ∪ jro0 → ⟪jvalid0 := true; gstore1 := gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))] [nx.last, gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))][nx.last] .ladrlist:= (gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))][nx.last].ladrlist + lax) ]; if err = ESUCCESS then {jmaxino0 := jmaxino0 + # ndx; if jvalid1 then let err0 = ? in index_sync#(fi2, fi1, jro0, gstore1, gstore0, nx0, pmaxino, p_os; ; jvalid, err0)} else jvalid0 := false⟫ ( (jvalid0 → valid-journal-head(nx0, gstore1, jro0)) ∧ fi2.lebs ⊆ dom gstore1 ∧ refsize-cons(gstore1, range fi2) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore2 ⊆ dom gstore1 ∧ ( err = ESUCCESS → # ax = # ndx ∧ ¬ dups(ax) ∧ nodes-cons(ax, ndx, gstore1, jro0) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx1, gstore2 ↓) + ax ∧ nodes(gstore1 ↓, jro0) = nodes(gstore2 ↓, jro1)[ax, ndx] ∧ new(ax, nodes(gstore2 ↓, jro1))) ∧ (err ≠ ESUCCESS → abs-log(nx0, gstore1 ↓) = abs-log(nx1, gstore2 ↓) ∧ nodes(gstore1 ↓, jro0) = nodes(gstore2 ↓, jro1)))), nx = [], nx0 = [], pmaxino = 0, dups(gstore[nx.last].ladrlist + lax), dups(nx0), dups(nx1)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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