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Proof step 21 from proof inv-flashsize-append (previous step)

# x = # lax, (lax + @(m, a.flashsize) ')[n] = @(m0, m1), n ≤ # lax, ∀ n. n < # lax → lax[n].size = x[n].flashsize ⊦ m1 = (x + a ')[n].flashsize

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del name: get-append-grt seq: ⊦ ¬ n < # x → (x + y)[n] = y[n - # x] subst: [n, y, x] → [n, a ', x] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m ≤ m; (s)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ n = # lax → (lax + ladr ')[n] = ladr; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ m - m = 0; (s)% ⊦ a '[0] = a; (s) Used terms: n, a ', x