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Proof step 14 from proof prefix-at (previous step)

# x = # lax, # x0 = # lax0, st0[m] = mkblock(x, lax, m2), st1[m] = mkblock(x0, lax0, m3), @(m0, m1) ∈ lax, m ∈ st0, m ∈ st1, x ⊑ x0, lax ⊑ lax0, ∀ n. n ∈ st0 → n ∈ st1 ⊦ x[pos(@(m0, m1), lax)] = st1[@(m, m0, m1)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ ladr ∈ lax ↔ (∃ lax0, lax1. lax = lax0 + ladr ' + lax1 ∧ ¬ ladr ∈ lax0)
Proof step 16:
# x0 = # lax0, # x = # lax, st1[m] = mkblock(x0, lax0, m3), st0[m] = mkblock(x, lax, m2), m ∈ st1, m ∈ st0, lax ⊑ lax0, x ⊑ x0, ∀ n. n ∈ st0 → n ∈ st1, ∃ lax0, lax1. lax = lax0 + @(m0, m1) ' + lax1 ∧ ¬ @(m0, m1) ∈ lax0 ⊦ x[pos(@(m0, m1), lax)] = st1[@(m, m0, m1)]

Rule argument

spec: list, inst: laddress-list name: firstoc-rew seq: ⊦ ladr ∈ lax ↔ (∃ lax0, lax1. lax = lax0 + ladr ' + lax1 ∧ ¬ ladr ∈ lax0) subst: [lax, ladr] → [lax, @(m0, m1)] flags: <all paths>

Additional information

Used terms: lax, @(m0, m1)