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Proof step 5 from proof btree-clean-fwd-strong (previous step)

((btree(rp1, r1, adr, height1, false, ri1, iast1, alladrs1, alladrs1, nstat) * P1))(zh1), ((btree(rp0, r0, adr, 0, false, ri0, iast0, ∅ ++ adr, ∅ ++ adr, nstat) * P0))(zh0), adr ∈ iast0, iast0 ⊆ iast1, alladrs1 ⊆ dom iast1 ⊦ 0 = height1 ∧ ri0 = ri1 ∧ ∅ ++ adr = alladrs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ((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))
Proof step 7:
((btree(rp1, r1, adr, height1, false, ri1, iast1, alladrs1, alladrs1, nstat) * P1))(zh1), adr ∈ iast0, alladrs1 ⊆ dom iast1, iast0 ⊆ iast1, ∃ r, zh, zbrar, dirty, nused. (r0 = null ⊃ ¬ dirty ∧ P0(zh0);r = r0 ∧ zh = zh0) ∧ (dirty → false) ∧ (adr ∈ ∅ ++ adr ↔ ¬ dirty) ∧ adr ∈ ∅ ++ adr ∧ nsize(nused, nstat) ∧ unmodified(adr, mkznode(rp0, zbrar, 0 = 0, dirty, nused), iast0) ∧ (( r => mkznode(rp0, zbrar, 0 = 0, dirty, nused) * bnode(r, zbrar, 0, nused, nused, 0, dirty, ri0, iast0, (∅ ++ adr) -- adr, (∅ ++ adr) -- adr) * P0) )(zh) ⊦ 0 = height1 ∧ ri0 = ri1 ∧ ∅ ++ adr = alladrs1

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] → [zh0, P0, nstat, ∅ ++ adr, ∅ ++ adr, iast0, ri0, false, 0, adr, r0, rp0] flags: <all paths>

Additional information

Used terms: zh0, P0, nstat, ∅ ++ adr, ∅ ++ adr, iast0, ri0, false, 0, adr, r0, rp0