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Proof step 3 from proof inv-sync (previous step)

remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), istore0 ⊑ istore, ¬ dups(nx), pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → syn ⊦ ⟪apersistence_sync#(adr, istore, istore0, ginval, gstore, gstore0, nx, maxino, ginval0; pstate, syn; err)⟫ ( (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
ginval = ginval1, ginval0 = ginval2, gstore = gstore1, gstore0 = gstore2, istore = istore1, istore0 = istore2, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval2), istore1 ⊑ istore2, pstate = unbuffered → syn, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2 ⊦ ⟪if pstate = readonly then err := EROFS else if pstate = unbuffered then err := ESUCCESS else {fail_or_success#(; ; err); syn := err = ESUCCESS; skip or pstate := readonly}⟫ ( (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn)), dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: sync: ⊦ ;