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Proof step 7 from proof size-append (previous step)

⊦ # ⌜x + x0⌝ = ⌜# x⌝ + ⌜# x0⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: size-fin seq: ⊦ # ⌜x⌝ = ⌜# x⌝ subst: [x] → [x + x0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(x + y) = # x + # y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ⌜n⌝ + n∞1 = ⌜n⌝ + n∞2 ↔ n∞1 = n∞2; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf Used terms: x + x0