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Proof step 2 from proof prefix-app-03 (previous step)

x + y + z ⊑ y ⊦ x = [] ∧ z = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-last inst: name: prefix-longer-01 seq: ⊦ # y < # x → ¬ x ⊑ y subst: [y, x] → [y, x + y + z] flags: rewrite, current

Additional information

Used simplifier rules: len: ⊦ #(x + y) = # x + # y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%le-add: ⊦ m + m0 ≤ m ↔ m0 = 0; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2%l: ⊦ # x = 0 ↔ x = []; from specification list-data Used terms: y, x + y + z