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Proof step 4 from proof inv-add-gnds (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
pstate = journal(nx.last), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, nx ≠ [], 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) ⊦ ⟪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))

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ journal(m).index?; (s)% ⊦ journal(m).journal?; (s)% ⊦ unbuffered ≠ journal(m); (s)