[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 14 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), nx.last ∈ gstore, # lax ≤ # gndx, istore1 ⊑ istore2, ⌊err⌋ ∨ err = ESUCCESS ⊦ ⟪ax := lax.to-adr(pstate.lnum), err0 := err; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax, gndx); gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist + lax; if err0 ≠ 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 15:
err = ESUCCESS ↔ # lax = # gndx, ginval = ginval1, ginval0 = ginval2, istore = istore1, istore0 = istore2, pstate = journal(nx.last), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval2, inv(gstore \ ginval2), inv(gstore0), inv(istore2), inv(istore1), inv(gstore[nx.last]), inv-flashsize(prefixn(# lax, gndx), lax), nx.last ∈ gstore, # lax ≤ # gndx, istore1 ⊑ istore2, pstate.index? ∨ pstate.journal?, ⌊err⌋ ∨ err = ESUCCESS ⊦ ⟪gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax, gndx); gstore[pstate.lnum].ladrlist := gstore[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(gstore[pstate.lnum].ladrlist + lax), dups(nx)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ journal(m).lnum = m; (s)% ⊦ journal(m).journal?; (s)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s)