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Proof step 7 from proof prefix-append-in (previous step)

# lax0 = # y, st[n] = mkblock(x, lax, m0), st0[n1] = mkblock(x0, lax1, m), n1 ∈ st[n, mkblock(x + y, lax + lax0, n0)], n1 ∈ st0, n ∈ st, dom st0 ⊆ dom st, ∀ n. n ∈ st0 ∧ n ∈ st → st0[n].list ⊑ st[n].list ∧ st0[n].ladrlist ⊑ st[n].ladrlist ∧ # st0[n].list = # st0[n].ladrlist ∧ # st[n].list = # st[n].ladrlist ⊦ x0 ⊑ st[n, mkblock(x + y, lax + lax0, n0)][n1].list ∧ lax1 ⊑ st[n, mkblock(x + y, lax + lax0, n0)][n1].ladrlist ∧ # x0 = # lax1 ∧ # st[n, mkblock(x + y, lax + lax0, n0)][n1].list = # st[n, mkblock(x + y, lax + lax0, n0)][n1].ladrlist

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
# lax0 = # y, st0[n1] = mkblock(x0, lax1, m), st[n] = mkblock(x, lax, m0), st[n, mkblock(x + y, lax + lax0, n0)][n1] = mkblock(x1, lax2, m1), n ∈ st, n1 ∈ st0, n1 ∈ st[n, mkblock(x + y, lax + lax0, n0)], dom st0 ⊆ dom st, ∀ n. n ∈ st0 ∧ n ∈ st → st0[n].list ⊑ st[n].list ∧ st0[n].ladrlist ⊑ st[n].ladrlist ∧ # st0[n].list = # st0[n].ladrlist ∧ # st[n].list = # st[n].ladrlist ⊦ x0 ⊑ x1 ∧ lax1 ⊑ lax2 ∧ # x0 = # lax1 ∧ # x1 = # lax2

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, lax, m] → [st[n, mkblock(x + y, lax + lax0, n0)][n1], x1, lax2, m1]

Additional information

Used simplifier rules: ⊦ (x = ablock.list ∧ lax = ablock.ladrlist) ∧ m = ablock.ref-size ↔ ablock = mkblock(x, lax, m); (elim) Used terms: st[n, mkblock(x + y, lax + lax0, n0)][n1], x1, lax2, m1