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Proof step 12 from proof to-adrs-sublist (previous step)

m1 ≤ # lax0, ∀ n0, n1, n. n0 + n1 ≤ # lax0 → sublist(n0, n1, lax0.to-adr(n)) = sublist(n0, n1, lax0).to-adr(n) ⊦ @(n, m, m0) ' + sublist(0, m1, lax0.to-adr(n)) = sublist(0, m1 + 1, @(m, m0) ' + lax0).to-adr(n)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del, inst: laddress-list name: sublist-append-02 seq: ⊦ # lax ≤ m → sublist(0, m, lax + lax0) = lax + sublist(0, m - # lax, lax0) subst: [lax0, lax, m] → [lax0, @(m, m0) ', m1 + 1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # ladr ' = 0 +1; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m < n → ¬ m + m0 < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: lax0, @(m, m0) ', m1 + 1