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Proof step 10 from proof nodes-alloc (previous step)

st[n, mkblock([], [], m)][m0] = mkblock(x, lax, m3) ⊦ n ∈ st, (m0 ∈ st[n, mkblock([], [], m)] ∧ @(m1, m2) ∈ lax → @(m0, m1, m2) ∈ st) ∧ (m0 ∈ st[n, mkblock([], [], m)] ∧ @(m1, m2) ∈ lax → st[n, mkblock([], [], m)][@(m0, m1, m2)] = nodes(st)[@(m0, m1, m2)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ∈ st[n0, ablock] ↔ n = n0 ∨ n ∈ st
Proof step 12:
st[n, mkblock([], [], m)][m0] = mkblock(x, lax, m3) ⊦ n ∈ st, ((m0 = n ∨ m0 ∈ st) ∧ @(m1, m2) ∈ lax → @(m0, m1, m2) ∈ st) ∧ ((m0 = n ∨ m0 ∈ st) ∧ @(m1, m2) ∈ lax → st[n, mkblock([], [], m)][@(m0, m1, m2)] = nodes(st)[@(m0, m1, m2)])

Rule argument

spec: store, inst: ablock-store-nat-store name: In-insert seq: ⊦ n ∈ st[n0, ablock] ↔ n = n0 ∨ n ∈ st subst: [ablock, n0, st, n] → [mkblock([], [], m), n, st, m0] flags: <all paths>

Additional information

Used terms: mkblock([], [], m), n, st, m0