34 lines
1 KiB
Text
34 lines
1 KiB
Text
import Lean
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def f (a : Nat) := a + a + a
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def g (a : Nat) := a + a
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def h (n : Nat) : Prop :=
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match n with
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| 0 => f 0 = f 1
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| n+1 => f (n+1) = f n ∧ g (2*n + 1) = g (2*n) ∧ h n
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-- Prints the equivalence class containing a `f` application
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open Lean Meta Elab Tactic Grind in
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elab "grind_test" n:num : tactic => withMainContext do
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let n := n.getNat
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let declName := (← Term.getDeclName?).getD `_main
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Meta.Grind.preprocessAndProbe (← getMainGoal) declName do
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let f0 ← Grind.shareCommon (mkApp (mkConst ``f) (mkNatLit 0))
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-- The `f 0` equivalence class contains `n+1` elements
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assert! (← getEqc f0).length == n + 1
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forEachENode fun node => do
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if node.self.isAppOf ``g then
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-- Any equivalence class containing a `g`-application contains 2 elements
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assert! (← getEqc (← getRoot node.self)).length == 2
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set_option grind.debug true in
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example : h 5 → False := by
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simp [h]
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grind_test 5
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sorry
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set_option maxRecDepth 2048
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example : h 100 → False := by
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simp [h]
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grind_test 100
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sorry
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