Definition instr_approx_rel (n:nat) (i1 i2:instruction) : Prop :=
  fmap_instr (K.approx n) i1 = fmap_instr (K.approx n) i2.

Lemma collapse_instr_approx : forall n m i, fmap_instr (K.approx n) (fmap_instr (K.approx m) i) = fmap_instr (K.approx (min n m)) i.