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Proof step 3 from proof refine-read-gnd (previous step)

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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
adr = @(m, m0, m1), gnd = gnd0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore2) = gstore2, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, btree-inv(rp, adr0, istore, istore0, zh, fi, fi0), inv(istore0), inv(istore), inv(gstore2), inv(gstore0 \ ginval0), ri-inj(fi0), ri-inj(fi), adr ∈ gstore0, istore0 ⊑ istore, pstate = unbuffered → syn0, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore0 ⊦ ⟪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), dups(nx0), m ∈ ginval0

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [adr, m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: adr, m, m0, m1