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Proof step 7 from proof at-write-same (previous step)

st[n] = mkblock(x, lax, m3), st[m0] = mkblock(x0, lax0, m4), n ∈ st, m0 ∈ st, @(m1, m2) ∈ lax0 ⊦ st[n, mkblock(x, lax, m)][@(m0, m1, m2)] = x0[pos(@(m1, m2), lax0)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ adr ∈ st → st[adr] = st[adr.lnum].list[pos(@(adr.pos, adr.size), st[adr.lnum].ladrlist)]
Proof step 9:
st[m0] = mkblock(x0, lax0, m4), st[n] = mkblock(x, lax, m3), @(m1, m2) ∈ lax0, m0 ∈ st, n ∈ st, @(m0, m1, m2) ∈ st[n, mkblock(x, lax, m)] ⊦ st[n, mkblock(x, lax, m)][@(m0, m1, m2).lnum].list [pos(@(@(m0, m1, m2).pos, @(m0, m1, m2).size), st[n, mkblock(x, lax, m)][@(m0, m1, m2).lnum].ladrlist) ] = x0[pos(@(m1, m2), lax0)]

Rule argument

spec: <toplevel> name: at seq: ⊦ adr ∈ st → st[adr] = st[adr.lnum].list [pos(@(adr.pos, adr.size), st[adr.lnum].ladrlist) ] subst: [adr, st] → [@(m0, m1, m2), st[n, mkblock(x, lax, m)]] flags: <all paths>

Additional information

Used simplifier rules: in-write-same: st[n].list = x, st[n].ladrlist = lax ⊦ n ∈ st → (adr ∈ st[n, mkblock(x, lax, m)] ↔ adr ∈ st);%in-in-adr: ⊦ st[n] = mkblock(x, lax, m0) ∧ n ∈ st ∧ @(n0, n1) ∈ lax → @(n, n0, n1) ∈ st;% ⊦ mkblock(x, lax, m).list = x; (s)% ⊦ mkblock(x, lax, m).ladrlist = lax; (s) Used terms: @(m0, m1, m2), st[n, mkblock(x, lax, m)]