f869902a4b
This came up in the context of simplifying proof states for https://github.com/leanprover/LNSym.
135 lines
4.3 KiB
Text
135 lines
4.3 KiB
Text
variable (a b : Nat)
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/- bitwise operation tests -/
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#check_simp (3 : Nat) &&& (1 : Nat) ~> 1
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#check_simp (3 : Nat) ^^^ (1 : Nat) ~> 2
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#check_simp (2 : Nat) ||| (1 : Nat) ~> 3
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#check_simp (3 : Nat) <<< (2 : Nat) ~> 12
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#check_simp (3 : Nat) >>> (1 : Nat) ~> 1
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/- subtract diff tests -/
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#check_simp (1000 : Nat) - 400 ~> 600
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#check_simp (a + 1000) - 1000 ~> a
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#check_simp (a + 400) - 1000 ~> a - 600
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#check_simp (a + 1000) - 400 ~> a + 600
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#check_simp 1000 - (a + 400) ~> 600 - a
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#check_simp 400 - (a + 1000) ~> 0
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#check_simp (a + 1000) - (b + 1000) ~> a - b
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#check_simp (a + 1000) - (b + 400) ~> a + 600 - b
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#check_simp (a + 400) - (b + 1000) ~> a - (b + 600)
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/- eq tests -/
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#check_simp (1234567 : Nat) = 123456 ~> False
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#check_simp (1234567 : Nat) = 1234567 ~> True
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#check_simp (123456 : Nat) = 1234567 ~> False
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#check_simp (a + 1000) = 1000 ~> a = 0
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#check_simp (a + 1000) = 400 ~> False
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#check_simp (a + 400) = 1000 ~> a = 600
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#check_simp 1000 = (a + 1000) ~> a = 0
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#check_simp 400 = (a + 1000) ~> False
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#check_simp 1000 = (a + 400) ~> a = 600
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#check_simp (a + 1000) = (b + 1000) ~> a = b
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#check_simp (a + 1000) = (b + 400) ~> a + 600 = b
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#check_simp (a + 400) = (b + 1000) ~> a = b + 600
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#check_simp (Nat.add a 400) = (Add.add b 1000) ~> a = b + 600
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#check_simp (Nat.add a 400) = b.succ.succ ~> a + 398 = b
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/- ne -/
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#check_simp 1000 ≠ (a + 1000) ~> a ≠ 0
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#check_simp (1234567 : Nat) ≠ 123456 ~> True
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#check_simp (a + 400) ≠ (b + 1000) ~> a ≠ b + 600
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/- leq -/
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#check_simp (1234567 : Nat) ≤ 123456 ~> False
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#check_simp (1234567 : Nat) ≤ 1234567 ~> True
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#check_simp (123456 : Nat) ≤ 1234567 ~> True
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#check_simp (a + 1000) ≤ 1000 ~> a = 0
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#check_simp (a + 1000) ≤ 400 ~> False
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#check_simp (a + 400) ≤ 1000 ~> a ≤ 600
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#check_simp 1000 ≤ (a + 1000) ~> True
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#check_simp 400 ≤ (a + 1000) ~> True
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#check_simp 1000 ≤ (a + 400) ~> 600 ≤ a
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#check_simp (a + 1000) ≤ (b + 1000) ~> a ≤ b
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#check_simp (a + 1000) ≤ (b + 400) ~> a + 600 ≤ b
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#check_simp (a + 400) ≤ (b + 1000) ~> a ≤ b + 600
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#check_simp (Nat.add a 400) ≤ (Add.add b 1000) ~> a ≤ b + 600
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#check_simp (Nat.add a 400) ≤ b.succ.succ ~> a + 398 ≤ b
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/- ge (just make sure le rules apply) -/
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#check_simp (123456 : Nat) ≥ 1234567 ~> False
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#check_simp (a + 400) ≥ 1000 ~> a ≥ 600
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#check_simp 1000 ≥ (a + 1000) ~> a = 0
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#check_simp (a + 1000) ≥ (b + 400) ~> a + 600 ≥ b
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/- beq tests -/
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#check_simp (1234567 : Nat) == 123456 ~> false
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#check_simp (1234567 : Nat) == 1234567 ~> true
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#check_simp (123456 : Nat) == 1234567 ~> false
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#check_simp (a + 1000) == 1000 ~> a == 0
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#check_simp (a + 1000) == 400 ~> false
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#check_simp (a + 400) == 1000 ~> a == 600
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#check_simp 1000 == (a + 1000) ~> a == 0
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#check_simp 400 == (a + 1000) ~> false
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#check_simp 1000 == (a + 400) ~> a == 600
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#check_simp (a + 1000) == (b + 1000) ~> a == b
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#check_simp (a + 1000) == (b + 400) ~> a + 600 == b
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#check_simp (a + 400) == (b + 1000) ~> a == b + 600
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/- bne tests -/
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#check_simp (1234567 : Nat) != 123456 ~> true
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#check_simp (a + 1000) != 1000 ~> a != 0
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#check_simp (a + 1000) != 400 ~> true
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#check_simp (a + 400) != 1000 ~> a != 600
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#check_simp 1000 != (a + 1000) ~> a != 0
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#check_simp 400 != (a + 1000) ~> true
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#check_simp 1000 != (a + 400) ~> a != 600
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#check_simp (a + 1000) != (b + 1000) ~> a != b
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#check_simp (a + 1000) != (b + 400) ~> a + 600 != b
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#check_simp (a + 400) != (b + 1000) ~> a != b + 600
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/-! Alterate instance tests
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These check that the simplification rules will matching
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offets still trigger even when the expression for the
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index is definition equal but not syntactically equal
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to the defualt instance.
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This can be relevant in Mathlib when rewriting using
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theorems involving algebraic hierarchy classes.
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-/
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class AddCommMagma (G : Type u) extends Add G where
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add_comm : ∀(x y : G), x + y = y + x
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instance instAddExtNat : AddCommMagma Nat where
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add_comm := Nat.add_comm
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#check_tactic @Add.add _ instAddExtNat.toAdd a 1 = 4 ~> a = 3 by simp only [Nat.succ.injEq]
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#check_tactic @HAdd.hAdd _ _ _ (@instHAdd _ instAddExtNat.toAdd) a 1 = 4 ~> a = 3 by simp only [Nat.succ.injEq]
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#check_tactic @Add.add _ instAddNat a 1 = 4 ~> a = 3 by simp
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#check_tactic @Add.add _ instAddExtNat.toAdd a 1 = 4 ~> a = 3 by simp
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#check_tactic @HAdd.hAdd _ _ _ (@instHAdd _ instAddExtNat.toAdd) a 1 = 4 ~> a = 3 by simp
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