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Proof step 10 from proof inv-add-gnds (previous step)

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

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 11:
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]), nx.last ∈ gstore, istore1 ⊑ istore2 ⊦ ⟪if pstate.journal? ∨ pstate = readonly then if pstate = readonly then err0 := EROFS else {choose lax, err with (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(gstore[pstate.lnum].ladrlist + lax) ∧ # lax ≤ # gndx ∧ inv-flashsize(prefixn(# lax, gndx), lax) ∧ (err = ESUCCESS ↔ # lax = # gndx) in {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 := ?} else abort⟫ ( 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)

Rule argument

pos: right 1

Additional information

Used simplifier rules: add-gnds: ⊦ ;