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Proof step 7 from proof to-adrs-sublist (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ # ax ≤ m → sublist(0, m, ax + ax0) = ax + sublist(0, m - # ax, ax0)
Proof step 9:
n1 ≤ # lax0 + 1, # @(n, m, m0) ' ≤ n1, ∀ 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, n1 - # @(n, m, m0) ', lax0.to-adr(n)) = sublist(0, n1, @(m, m0) ' + lax0).to-adr(n)

Rule argument

spec: list-del, inst: address-list-set name: sublist-append-02 seq: ⊦ # ax ≤ m → sublist(0, m, ax + ax0) = ax + sublist(0, m - # ax, ax0) subst: [ax0, ax, m] → [lax0.to-adr(n), @(n, m, m0) ', n1] flags: <all paths>

Additional information

Used simplifier rules: adrs-empty: ⊦ ([]).to-adr(n) = [];% ⊦ # adr ' = 0 +1; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ sublist(0, 0, ax) = []; (s)% ⊦ sublist(0, 0, lax) = []; (s) Used terms: lax0.to-adr(n), @(n, m, m0) ', n1