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Proof step 13 from proof blastN-rec-01 (previous step)

n = m + 1, n ≤ # y + 1, ∀ x0, n, a. # x0 < #(y + a0 ') → n ≤ # x0 → butlastn(n, a ' + x0) = a ' + butlastn(n, x0) ⊦ n = 0, butlastn(m, a ' + y) = a ' + butlastn(n, y + a0 ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
m ≤ # y, ∀ x0, n, a. # x0 < #(y + a0 ') → n ≤ # x0 → butlastn(n, a ' + x0) = a ' + butlastn(n, x0) ⊦ butlastn(m, a ' + y) = a ' + butlastn(m, y)

Rule argument

Additional information

Used simplifier rules: butlastN-rec: ⊦ butlastn(n + 1, x) = butlastn(n, x.butlast);%butlast-def: ⊦ (x + a ').butlast = x;%lep-02: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; from specification nat%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2