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Proof step 16 from proof inv-add-gnds (previous step)

err = ESUCCESS ↔ # lax = # gndx, ginval = ginval1, ginval0 = ginval2, istore = istore1, istore0 = istore2, pstate = journal(nx.last), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval2, inv(gstore[nx.last]), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval2), inv-flashsize(prefixn(# lax, gndx), lax), pstate.lnum ∈ gstore, nx.last ∈ gstore, # lax ≤ # gndx, istore1 ⊑ istore2, ⌊err⌋ ∨ err = ESUCCESS, pstate.index? ∨ pstate.journal? ⊦ ⟪gstore := gstore[pstate.lnum, gstore[pstate.lnum].gndlist:= (gstore[pstate.lnum].gndlist + prefixn(# lax, gndx))] [pstate.lnum, gstore[pstate.lnum, gstore[pstate.lnum].gndlist:= (gstore[pstate.lnum].gndlist + prefixn(# lax, gndx))][pstate.lnum] .ladrlist:= ( gstore[pstate.lnum, gstore[pstate.lnum].gndlist:= (gstore[pstate.lnum].gndlist + prefixn(# lax, gndx))][pstate.lnum] .ladrlist + lax) ]; if err ≠ ESUCCESS then ax := ?, pstate := readonly; syn := ?⟫ ( inv(gstore \ ginval2) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval2 ∧ (pstate.journal? → pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn)), nx = [], dups(nx), dups(gstore[pstate.lnum].ladrlist + lax)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 17:
err = ESUCCESS ↔ # lax = # gndx, ginval = ginval1, ginval0 = ginval2, gstore = gstore1[pstate.lnum, gstore1[pstate.lnum].gndlist:= (gstore1[pstate.lnum].gndlist + prefixn(# lax, gndx))] [pstate.lnum, gstore1[pstate.lnum, gstore1[pstate.lnum].gndlist:= (gstore1[pstate.lnum].gndlist + prefixn(# lax, gndx))][pstate.lnum] .ladrlist:= ( gstore1[pstate.lnum, gstore1[pstate.lnum].gndlist:= (gstore1[pstate.lnum].gndlist + prefixn(# lax, gndx))][pstate.lnum].ladrlist + lax) ], istore = istore1, istore0 = istore2, pstate = journal(nx.last), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore1 ∪ ginval2, inv(gstore1 \ ginval2), inv(gstore0), inv(istore2), inv(istore1), inv(gstore1[nx.last]), inv-flashsize(prefixn(# lax, gndx), lax), nx.last ∈ gstore1, pstate.lnum ∈ gstore1[pstate.lnum, gstore1[pstate.lnum].gndlist:= (gstore1[pstate.lnum].gndlist + prefixn(# lax, gndx))], pstate.lnum ∈ gstore1, # lax ≤ # gndx, istore1 ⊑ istore2, ⌊err⌋ ∨ err = ESUCCESS, pstate.index? ∨ pstate.journal? ⊦ ⟪if err ≠ ESUCCESS then ax := ?, pstate := readonly; syn := ?⟫ ( inv(gstore \ ginval2) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval2 ∧ (pstate.journal? → pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn)), nx = [], dups(gstore1[pstate.lnum].ladrlist + lax), dups(nx)

Rule argument

Additional information

Used simplifier rules: ⊦ journal(m).lnum = m; (s)% ⊦ ¬ journal(m).index?; (s)% ⊦ journal(m).journal?; (s)% ⊦ n ∈ gstore[n, gblock]; (s)