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Proof step 1 from proof butlast-len (conclusion)

⊦ # (a ' + x).butlast = # x

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-last inst: name: lb seq: ⊦ x ≠ [] → # x.butlast = # x - 1 subst: [x] → [a ' + x] flags: rewrite, current

Additional information

Used simplifier rules: len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%app-02-ant: ⊦ ¬ x + y ≠ [] ↔ x = [] ∧ y = []; from specification list%e: ⊦ a ' ≠ []; from specification list Used terms: a ' + x