[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 28 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, height, false, ri, nodes(istore0), alladrs, alladrs, ok) * true))(zh), inv(istore0), inv(istore), refsize-cons(istore, alladrs), refsize-cons(istore0, alladrs), adr ∈ istore, alladrs ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore0), istore0 ⊑ istore, rp = null ∨ ¬ dirty, ¬ dirty ∨ rp = null ⊦ ((btree(null, null, adr, height, false, ri, nodes(remove-refsize0(istore)), alladrs, alladrs, ok) * true))(zh), nodes(istore) | alladrs ⊆ nodes(remove-refsize0(istore))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ refsize-cons(istore, as) ∧ as ⊆ dom nodes(istore) ∧ valid-adrs(as) → nodes(istore) | as ⊆ nodes(remove-refsize0(istore))

Rule argument

spec: ablock-store-refsize-cons, inst: index-store name: remove-refsize0-subset-refed seq: ⊦ refsize-cons(istore, as) ∧ as ⊆ dom nodes(istore) ∧ valid-adrs(as) → nodes(istore) | as ⊆ nodes(remove-refsize0(istore)) subst: [as, istore] → [alladrs, istore] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inv(istore) ∧ as ⊆ dom nodes(istore) → valid-adrs(as); (ss) Used terms: alladrs, istore