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Proof step 9 from proof to-adrs-sublist (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
1 ≤ n1, n1 ≤ # lax0 + 1, ∀ 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 - 1, lax0.to-adr(n)) = sublist(0, n1, @(m, m0) ' + lax0).to-adr(n), n1 = 0

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ # adr ' = 0 +1; (s)