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Proof step 3 from proof inv-add-ind (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, pstate.index? ∨ pstate = readonly ⊦ ⟪apersistence_add_ind#(ind, adr, istore0, ginval, gstore, gstore0, nx, maxino, ginval0; adr0, istore, pstate, syn; err)⟫ ( inv(istore) ∧ istore0 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), istore0 ⊑ istore, pstate = unbuffered → syn, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore, pstate.index? ∨ pstate = readonly ⊦ ⟪apersistence_add_ind#(ind, adr, istore0, ginval, gstore, gstore0, nx, maxino, ginval0; adr0, istore, pstate, syn; err)⟫ ( inv(istore) ∧ istore0 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn)), pstate.index?, dups(nx)
Proof step 9:
pstate = index(m), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, pstate.index?, inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), istore0 ⊑ istore, pstate = unbuffered → syn, pstate.index? → m ∈ istore, pstate.journal? → nx ≠ [] ∧ m = nx.last ∧ m ∈ gstore, pstate.index? ∨ pstate = readonly ⊦ ⟪apersistence_add_ind#(ind, adr, istore0, ginval, gstore, gstore0, nx, maxino, ginval0; adr0, istore, pstate, syn; err)⟫ ( inv(istore) ∧ istore0 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn)), dups(nx)

Rule argument

spec: persistence-state name: elim-02 seq: ⊦ pstate.index? → (m = pstate.lnum ↔ pstate = index(m)) subst: [pstate, m] → [pstate, m]

Additional information

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