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Proof step 25 from proof inv-addn (previous step)

abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro), remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro0, dom gstore0 ∪ elems nx = dom gstore ∪ jro, nx0 ≠ [], pmaxino ≠ 0, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(gstore1[nx0.last]), inv(gstore1 \ jro0), inv(gstore \ jro), inv(gstore0), refsize-cons(gstore1, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range fi2), ri-inj(fi1), ri-inj(fi2), transaction(ndx, gndx), valid-journal-head(nx0, gstore1, jro0), nx0.last ∈ gstore1, pmaxino ≤ jmaxino1, dom gstore ⊆ dom gstore1, fi1.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore, fi2.lebs ⊆ dom gstore1, ¬ dups(nx), ¬ dups(nx0), jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ [index_add_gnds#(gndx, fi2, fi1, jro0, gstore0, nx0, pmaxino, p_os; ax, gstore1; jvalid, err)] ( inv(gstore1 \ jro0) ∧ dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro0 → ⟪jvalid0 := true; 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 gstore ⊆ dom gstore1 ∧ ( err = ESUCCESS → # ax = # ndx ∧ ¬ dups(ax) ∧ nodes-cons(ax, ndx, gstore1, jro0) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro)[ax, ndx] ∧ new(ax, nodes(gstore ↓, jro))) ∧ (err ≠ ESUCCESS → abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro))))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 26:
abs-log(nx0, gstore1 ↓) = abs-log(nx1, gstore2 ↓), fi = fi1, fi0 = fi2, gstore = gstore1, jro = jro0, nodes(gstore1 ↓, jro0) = nodes(gstore2 ↓, jro1), nx = nx0, remove-refsize0(gstore0) = gstore0, elems nx1 ∩ jro1 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro0 = ∅, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro0, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore0), inv(gstore2 \ jro1), inv(gstore1 \ jro0), inv(gstore1[nx0.last]), refsize-cons(gstore2, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore1, range fi2), ri-inj(fi2), ri-inj(fi1), transaction(ndx, gndx), valid-journal-head(nx0, gstore1, jro0), nx0.last ∈ gstore1, pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore0, dom gstore2 ⊆ dom gstore1, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ [if nx ≠ [] then {choose lax, err0 with (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ¬ dups(gstore[nx.last].ladrlist + lax) ∧ # lax ≤ # gndx ∧ inv-flashsize(prefixn(# lax, gndx), lax) ∧ (err0 = ESUCCESS ↔ # lax = # gndx) in {ax := lax.to-adr(nx.last), err := err0; gstore[nx.last].gndlist := gstore[nx.last].gndlist + prefixn(# lax, gndx); gstore[nx.last].ladrlist := gstore[nx.last].ladrlist + lax; if err ≠ ESUCCESS then ax := ?}; jvalid := ?} else abort] ( inv(gstore \ jro0) ∧ dom gstore0 ∪ elems nx0 = dom gstore ∪ jro0 → ⟪jvalid0 := true; gstore1 := gstore; 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)))), nx0 = [], pmaxino = 0, dups(nx1), dups(nx0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: index_add_gnds# (GNDLIST, PRI, PFI, PINVAL, PSTORE0, PNL, PMAXINO, P_OS ; ADRLIST, PSTORE ; ISYNCED, ERR ) {if PNL ≠ [] then {choose LADRLIST, ERR0 with (⌊ERR0⌋ ∨ ERR0 = ESUCCESS) ∧ ¬ dups(PSTORE[PNL.last].ladrlist + LADRLIST) ∧ # LADRLIST ≤ # GNDLIST ∧ inv-flashsize(prefixn(# LADRLIST, GNDLIST), LADRLIST) ∧ (ERR0 = ESUCCESS ↔ # LADRLIST = # GNDLIST) in {ADRLIST := LADRLIST.to-adr(PNL.last), ERR := ERR0; PSTORE[PNL.last].gndlist := PSTORE[PNL.last].gndlist + prefixn(# LADRLIST, GNDLIST); PSTORE[PNL.last].ladrlist := PSTORE[PNL.last].ladrlist + LADRLIST; if ERR ≠ ESUCCESS then ADRLIST := ?}; ISYNCED := ?} else abort };