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Proof step 13 from proof lastN-blastN (previous step)

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

User applied rule apply induction

And closed the goal!

Rule argument

subst: [x0, n] → [y, m]

Additional information

Used simplifier rules: len: ⊦ #(x + y) = # x + # y; from specification list%len-02: ⊦ # a ' = 0 +1; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: y, m