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Proof step 17 from proof to-adrs-sublist (previous step)

n2 + n1 ≤ # lax0, ∀ n0, n1, n. n0 + n1 ≤ # lax0 → sublist(n0, n1, lax0.to-adr(n)) = sublist(n0, n1, lax0).to-adr(n) ⊦ sublist(n2 + 1, n1, @(n, m, m0) ' + lax0.to-adr(n)) = sublist(n2 + 1, n1, @(m, m0) ' + lax0).to-adr(n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ # ax ≤ n ∧ n + m ≤ # ax + # ax0 → sublist(n, m, ax + ax0) = sublist(n - # ax, m, ax0)
Proof step 19:
n2 + n1 ≤ # lax0, # @(n, m, m0) ' ≤ n2 + 1, (n2 + 1) + n1 ≤ # @(n, m, m0) ' + # lax0.to-adr(n), ∀ n0, n1, n. n0 + n1 ≤ # lax0 → sublist(n0, n1, lax0.to-adr(n)) = sublist(n0, n1, lax0).to-adr(n) ⊦ sublist(n2 + 1 - # @(n, m, m0) ', n1, lax0.to-adr(n)) = sublist(n2 + 1, n1, @(m, m0) ' + lax0).to-adr(n)

Rule argument

spec: list-del, inst: address-list-set name: sublist-append-01-01 seq: ⊦ # ax ≤ n ∧ n + m ≤ # ax + # ax0 → sublist(n, m, ax + ax0) = sublist(n - # ax, m, ax0) subst: [ax0, ax, m, n] → [lax0.to-adr(n), @(n, m, m0) ', n1, n2 + 1] flags: <all paths>

Additional information

Used simplifier rules: addresslist-length: ⊦ # lax.to-adr(n) = # lax;% ⊦ # adr ' = 0 +1; (s)% ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n ≤ n0 ∧ n1 ≤ m → n + n1 ≤ n0 + m; (s) Used terms: lax0.to-adr(n), @(n, m, m0) ', n1, n2 + 1