qify tactic #
The qify tactic is used to shift propositions from ℕ or ℤ to ℚ.
This is often useful since ℚ has well-behaved division.
example (a b c x y z : ℕ) (h : ¬ x*y*z < 0) : c < a + 3*b := by
qify
qify at h
/-
h : ¬↑x * ↑y * ↑z < 0
⊢ ↑c < ↑a + 3 * ↑b
-/
sorry
The qify tactic is used to shift propositions from ℕ or ℤ to ℚ.
This is often useful since ℚ has well-behaved division.
example (a b c x y z : ℕ) (h : ¬ x*y*z < 0) : c < a + 3*b := by
qify
qify at h
/-
h : ¬↑x * ↑y * ↑z < 0
⊢ ↑c < ↑a + 3 * ↑b
-/
sorry
qify can be given extra lemmas to use in simplification. This is especially useful in the
presence of nat subtraction: passing ≤ arguments will allow push_cast to do more work.
example (a b c : ℤ) (h : a / b = c) (hab : b ∣ a) (hb : b ≠ 0) : a = c * b := by
qify [hab] at h hb ⊢
exact (div_eq_iff hb).1 h
qify makes use of the @[zify_simps] and @[qify_simps] attributes to move propositions,
and the push_cast tactic to simplify the ℚ-valued expressions.
Equations
- One or more equations did not get rendered due to their size.