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Proof step 2 from proof refine-read-gnd (previous step)

syn ↔ syn0, fi1 = fi0, ginval = ginval0, ginval1 = ginval2, gnd = gnd0, gstore = gstore0, gstore1 = gstore2, maxino = maxino0, nx = nx0, ri = fi, btree-inv(rp, adr0, istore, istore0, zh, ri, fi1), btree-inv(rp, adr0, istore, istore0, zh, fi, fi0), inv-index(istore, istore0), inv-journal(nx0, gstore0, gstore2, ginval0), inv-journal(nx, gstore, gstore1, ginval), inv-state(pstate, nx0, gstore0, istore, syn0), ri-inj(fi0), ri-inj(fi), adr ∈ gstore ⊦ ⟪btree_read_gnd#(adr, adr0, istore, istore0, ginval0, gstore0, gstore2, nx0, maxino0, ginval2, pstate, syn0; gnd; err)⟫ ⟨index_read_gnd#(adr, fi, fi0, ginval, gstore, gstore1, nx, maxino, ginval1, syn; gnd0; err0)⟩ ( ( ginval = ginval0 ∧ gstore = gstore0 ∧ gstore1 = gstore2 ∧ nx = nx0 ∧ maxino = maxino0 ∧ ginval1 = ginval2 ∧ btree-inv(rp, adr0, istore, istore0, zh, fi, fi0) ∧ ri = fi ∧ fi1 = fi0 ∧ (syn ↔ syn0)) ∧ gnd = gnd0 ∧ err = err0), adr.lnum ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
gnd = gnd0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore0) = istore0, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, btree-inv(rp, adr0, istore, istore0, zh, fi, fi0), inv(gstore0 \ ginval0), inv(gstore2), inv(istore), inv(istore0), ri-inj(fi), ri-inj(fi0), adr ∈ gstore0, istore0 ⊑ istore, ¬ dups(nx0), ¬ adr.lnum ∈ ginval0, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore0, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → syn0 ⊦ ⟪btree_read_gnd#(adr, adr0, istore, istore0, ginval0, gstore0, gstore2, nx0, maxino0, ginval2, pstate, syn0; gnd; err)⟫ ⟨index_read_gnd#(adr, fi, fi0, ginval0, gstore0, gstore2, nx0, maxino0, ginval2, syn0; gnd0; err0)⟩ (gnd = gnd0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)