[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 11 from proof btree-ri-unique (previous step)

((btree(rp, rp0, adr, 0, dirty, ri1, iast, as1, alladrs1, ok) * P1))(zh), ((btree(rp, rp0, adr, 0, dirty, ri0, iast, as0, alladrs0, ok) * P0))(zh), as1 ⊆ dom iast, as1 ⊆ alladrs1, as0 ⊆ dom iast, as0 ⊆ alladrs0 ⊦ ri0 = ri1, rp0 = null

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ((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 13:
((btree(rp, rp0, adr, 0, dirty, ri0, iast, as0, alladrs0, ok) * P0))(zh), as0 ⊆ alladrs0, as0 ⊆ dom iast, as1 ⊆ alladrs1, as1 ⊆ dom iast, ∃ r, zh1, zbrar, dirty1, nused. (rp0 = null ⊃ ¬ dirty1 ∧ P1(zh);r = rp0 ∧ zh1 = zh) ∧ (dirty1 → dirty) ∧ (adr ∈ as1 ↔ ¬ dirty1) ∧ adr ∈ alladrs1 ∧ nsize(nused, ok) ∧ unmodified(adr, mkznode(rp, zbrar, 0 = 0, dirty1, nused), iast) ∧ ((r => mkznode(rp, zbrar, 0 = 0, dirty1, nused) * bnode(r, zbrar, 0, nused, nused, 0, dirty1, ri1, iast, as1 -- adr, alladrs1 -- adr) * P1) )(zh1) ⊦ ri0 = ri1, rp0 = null

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, P1, ok, alladrs1, as1, iast, ri1, dirty, 0, adr, rp0, rp] flags: <all paths>

Additional information

Used terms: zh, P1, ok, alladrs1, as1, iast, ri1, dirty, 0, adr, rp0, rp