[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 prefix-del-right (previous step)

st[n] = mkblock(x, lax, m0), n ∈ st0, n ∈ st, dom st ⊆ dom st0, ∀ n. n ∈ st ∧ n ∈ st0 → st[n].list ⊑ st0[n].list ∧ st[n].ladrlist ⊑ st0[n].ladrlist ∧ # st[n].list = # st[n].ladrlist ∧ # st0[n].list = # st0[n].ladrlist ⊦ m ∈ st, x ⊑ st0[n].list ∧ lax ⊑ st0[n].ladrlist ∧ # x = # lax ∧ # st0[n].list = # st0[n].ladrlist

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
st[n] = mkblock(x, lax, m0), st0[n] = mkblock(x0, lax0, m1), n ∈ st, n ∈ st0, dom st ⊆ dom st0, ∀ n. n ∈ st ∧ n ∈ st0 → st[n].list ⊑ st0[n].list ∧ st[n].ladrlist ⊑ st0[n].ladrlist ∧ # st[n].list = # st[n].ladrlist ∧ # st0[n].list = # st0[n].ladrlist ⊦ m ∈ st, x ⊑ x0 ∧ lax ⊑ lax0 ∧ # x = # lax ∧ # x0 = # lax0

Rule argument

spec: ablock name: elim seq: ⊦ (x = ablock.list ∧ lax = ablock.ladrlist) ∧ m = ablock.ref-size ↔ ablock = mkblock(x, lax, m) subst: [ablock, x, m, m0, m1] → [st0[n], x0, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ (x = ablock.list ∧ lax = ablock.ladrlist) ∧ m = ablock.ref-size ↔ ablock = mkblock(x, lax, m); (elim) Used terms: st0[n], x0, m3, m4, m5