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Proof step 3 from proof crash-neutral-add-gnds (previous step)

gstore1 = crash(gstore, gstore0, ginval, nx), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, syn, 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.journal? ∨ pstate = readonly ⊦ ⟨apersistence_add_gnds#(gndx, adr0, istore, istore0, ginval, gstore0, nx, maxino0, ginval2; ax, gstore, pstate, syn; err)⟩ (syn ∧ gstore1 = crash(gstore, gstore0, ginval, nx))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
gstore1 = crash(gstore, gstore0, ginval, nx), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, syn, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore, pstate.journal? ∨ pstate = readonly ⊦ ⟨apersistence_add_gnds#(gndx, adr0, istore, istore0, ginval, gstore0, nx, maxino0, ginval2; ax, gstore, pstate, syn; err)⟩ (syn ∧ gstore1 = crash(gstore, gstore0, ginval, nx)), pstate.journal?, dups(nx)
Proof step 9:
gstore1 = crash(gstore, gstore0, ginval, nx), pstate = journal(m), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, syn, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, pstate.journal?, inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), istore0 ⊑ istore, pstate.index? → m ∈ istore, pstate.journal? → nx ≠ [] ∧ m = nx.last ∧ m ∈ gstore, pstate.journal? ∨ pstate = readonly ⊦ ⟨apersistence_add_gnds#(gndx, adr0, istore, istore0, ginval, gstore0, nx, maxino0, ginval2; ax, gstore, pstate, syn; err)⟩ (syn ∧ gstore1 = crash(gstore, gstore0, ginval, nx)), dups(nx)

Rule argument

spec: persistence-state name: elim-01 seq: ⊦ pstate.journal? → (m = pstate.lnum ↔ pstate = journal(m)) subst: [pstate, m] → [pstate, m]

Additional information

Used simplifier rules: ⊦ pstate.journal? → (m = pstate.lnum ↔ pstate = journal(m)); (elim) Used terms: pstate, m