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Proof step 3 from proof inv-add-gnds (previous step)

pstate.lnum = nx.last, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, nx ≠ [], pstate ≠ unbuffered, pstate.journal?, btree-inv(rp, adr, istore, istore0, zh, ri, fi), inv(gstore[nx.last]), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), nx.last ∈ gstore, istore0 ⊑ istore, ¬ dups(nx), pstate.index? → nx.last ∈ istore ⊦ ⟪btree_add_gnds#(adr, istore, istore0, ginval, gstore0, nx, maxino, ginval0; gndx, 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 elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
m = nx.last, pstate = journal(m), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, pstate.journal?, btree-inv(rp, adr, istore, istore0, zh, ri, fi), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(gstore[nx.last]), nx.last ∈ gstore, istore0 ⊑ istore, pstate.index? → nx.last ∈ istore ⊦ ⟪btree_add_gnds#(adr, istore, istore0, ginval, gstore0, nx, maxino, ginval0; gndx, 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)), nx = [], pstate = unbuffered, 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