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Proof step 18 from proof btree-inv-remove-refsize0 (previous step)

zh[rp] = mkznode(rp0, zbrar, boolvar, dirty, nused), ((btree(null, rp, adr, height, false, ri, nodes(istore), alladrs, alladrs, ok) * true))(zh), ((btree(null, null, adr, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), inv(istore), inv(istore0), refsize-cons(istore0, alladrs0), refsize-cons(istore, alladrs), adr ∈ istore, nodes(istore) | alladrs ⊆ nodes(remove-refsize0(istore)), alladrs0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), istore0 ⊑ istore, ¬ dirty ∨ rp = null, rp = null ∨ ¬ dirty ⊦ adr ∈ remove-refsize0(istore), adr ∈ alladrs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: btree seq: ⊦ (( btree (rp, r0, adr, height, dirty0, ri, iast, as, alladrs, nstat) * P) )(zh0) ↔ (∃ r, zh, zbrar, dirty, nused. (r0 = null ⊃ ¬ dirty ∧ P(zh0);r = r0 ∧ zh = zh0) ∧ (dirty → dirty0) ∧ (adr ∈ as ↔ ¬ dirty) ∧ adr ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified (adr, mkznode(rp, zbrar, height = 0, dirty, nused), iast) ∧ (( r => mkznode(rp, zbrar, height = 0, dirty, nused) * bnode (r, zbrar, 0, nused, nused, height, dirty, ri, iast, as -- adr, alladrs -- adr) * P) )(zh)) subst: [zh0, P, nstat, alladrs, as, iast, ri, dirty0, height, adr, r0, rp] → [zh, true, ok, alladrs, alladrs, nodes(istore), ri, false, height, adr, rp, null] flags: <all paths>

Additional information

Used terms: zh, true, ok, alladrs, alladrs, nodes(istore), ri, false, height, adr, rp, null