0dc317c73c
#5167 removed `reduceCtorEq` from the default simproc set. `norm_cast` relies on it, so we add it back in there.
87 lines
2.4 KiB
Text
87 lines
2.4 KiB
Text
@[coe] def Bool.toNat' : Bool → Nat
|
|
| true => 1
|
|
| false => 0
|
|
|
|
instance : Coe Bool Nat where
|
|
coe := Bool.toNat'
|
|
|
|
@[norm_cast] theorem ofNat_band (a b : Bool) : (↑(a && b) : Nat) = ↑a &&& ↑b := by
|
|
cases a <;> cases b <;> rfl
|
|
|
|
example (a b c : Bool) (n : Nat) (h : n = a &&& b &&& c)
|
|
: (↑(a && b && c) : Nat) = n := by
|
|
push_cast
|
|
guard_target =ₛ(↑a &&& ↑b &&& ↑c) = n
|
|
rw [h]
|
|
|
|
example (a b c : Bool) (n : Nat) (h : n = (a && b && c))
|
|
: (↑a &&& ↑b &&& ↑c) = n := by
|
|
norm_cast
|
|
guard_target =ₛ ↑(a && b && c) = n
|
|
rw [h]
|
|
|
|
|
|
set_option linter.missingDocs false
|
|
|
|
variable (an bn cn dn : Nat) (az bz cz dz : Int)
|
|
|
|
example : (an : Int) = bn → an = bn := by intro h; exact_mod_cast h
|
|
example : an = bn → (an : Int) = bn := by intro h; exact_mod_cast h
|
|
|
|
example : (an : Int) < bn ↔ an < bn := by norm_cast
|
|
example : (an : Int) ≠ (bn : Int) ↔ an ≠ bn := by norm_cast
|
|
|
|
-- zero and one cause special problems
|
|
example : az > (1 : Nat) ↔ az > 1 := by norm_cast
|
|
example : az > (0 : Nat) ↔ az > 0 := by norm_cast
|
|
|
|
example : (an : Int) ≠ 0 ↔ an ≠ 0 := by norm_cast
|
|
|
|
example (a b : Nat) (h : False) : (a : Int) < ((2 * b : Nat) : Int) := by
|
|
push_cast
|
|
guard_target = (a : Int) < 2 * (b : Int)
|
|
cases h
|
|
|
|
example : (an : Int) + bn = (an + bn : Nat) := by norm_cast
|
|
|
|
example (h : ((an + bn : Nat) : Int) = (an : Int) + (bn : Int)) : True := by
|
|
push_cast at h
|
|
guard_hyp h : (an : Int) + (bn : Int) = (an : Int) + (bn : Int)
|
|
trivial
|
|
|
|
example (h : ((an * bn : Nat) : Int) = (an : Int) * (bn : Int)) : True := by
|
|
push_cast at h
|
|
guard_hyp h : (an : Int) * (bn : Int) = (an : Int) * (bn : Int)
|
|
trivial
|
|
|
|
--testing numerals
|
|
example : ((42 : Nat) : Int) = 42 := by norm_cast
|
|
|
|
structure p (n : Int)
|
|
example : p 42 := by
|
|
norm_cast
|
|
guard_target = p 42
|
|
exact ⟨⟩
|
|
|
|
example : an + bn = 1 ↔ (an + bn : Int) = 1 := by norm_cast
|
|
|
|
example (h : bn ≤ an) : an - bn = 1 ↔ (an - bn : Int) = 1 := by norm_cast
|
|
|
|
example (k : Nat) {x y : Nat} (h : ((x + y + k : Nat) : Int) = 0) : x + y + k = 0 := by
|
|
push_cast at h
|
|
guard_hyp h : (x : Int) + y + k = 0
|
|
assumption_mod_cast
|
|
|
|
example (a b : Nat) (h2 : ((a + b + 0 : Nat) : Int) = 10) :
|
|
((a + b : Nat) : Int) = 10 := by
|
|
push_cast
|
|
push_cast [Int.add_zero] at h2
|
|
exact h2
|
|
|
|
theorem b (_h g : true) : true ∧ true := by
|
|
constructor
|
|
assumption_mod_cast
|
|
assumption_mod_cast
|
|
|
|
example : ¬n - k + 1 = 0 := by
|
|
norm_cast
|