[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 22 from proof inv-add-gnds (previous step)

err0 = ESUCCESS ↔ # lax = # gndx, err0 = ESUCCESS, fi = fi1, fi0 = fi2, ginval = ginval1, ginval0 = ginval2, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval2, inv(gstore[nx.last]), inv(gstore0), inv(gstore \ ginval2), inv-flashsize(prefixn(# lax, gndx), lax), ri-inj(fi1), ri-inj(fi2), nx.last ∈ gstore, nx.last ∈ gstore[nx.last, gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + prefixn(# lax, gndx))], # lax ≤ # gndx, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ nx = [], dups(nx), dups(gstore[nx.last].ladrlist + lax), 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) ] \ ginval2) ∧ dom gstore0 ∪ elems nx = 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) ] ∪ ginval2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# lax = # gndx, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval2, inv(gstore[nx.last]), inv(gstore0), inv(gstore \ ginval2), inv-flashsize(gndx, lax), ri-inj(fi1), ri-inj(fi2), nx.last ∈ gstore ⊦ nx = [], dups(lax), dups(gstore[nx.last].ladrlist), dups(nx), dups(gstore[nx.last].ladrlist + lax), inv((gstore[nx.last].gndlist:= (gstore[nx.last].gndlist + gndx)).ladrlist:= (gstore[nx.last].ladrlist + lax)), nx.last ∈ ginval2

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]%⊦ inv(gstore \ ns) → (inv(gstore[n, gblock] \ ns) ↔ n ∈ ns ∨ inv(gblock)); (ws)% ⊦ n ∈ gstore → dom gstore ++ n = dom gstore; (s)% ⊦ dom gstore[n, gblock] = dom gstore ++ n; (s)% ⊦ gstore[n, gblock][n, gblock0] = gstore[n, gblock0]; (s)% ⊦ (gblock.gndlist:= gndx).ladrlist = gblock.ladrlist; (s)% ⊦ gstore[n, gblock][n] = gblock; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ n ∈ gstore[n, gblock]; (s)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s)% ⊦ ¬ n < n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)