29 lines
997 B
Text
29 lines
997 B
Text
import Lean
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open Lean in open Lean.Meta in
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def test (declName : Name) : MetaM Unit := do
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let info ← getConstInfo declName
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forallTelescopeReducing info.type fun _ e => do
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let some (e', p) ← Linear.Nat.simpCnstr? e | throwError "failed to simplify{indentExpr e}"
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check p
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unless (← isDefEq (← inferType p) (← mkEq e e')) do
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throwError "invalid proof"
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IO.println s!"{← Meta.ppExpr e} ==> {← Meta.ppExpr e'}"
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axiom ex1 (a b : Nat) : a + b + 1 + a < b + 4 + a
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axiom ex2 (a b : Nat) : a + b + 1 + a = b + 4 + a + b
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axiom ex3 (a b : Nat) : 5 = b + 4 + a + b
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axiom ex4 (a b : Nat) : 4 = 1 + a
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axiom ex5 (a b : Nat) : 4 + ((a + a) + b) + (a + a) + (b + b) ≤ 3 + (4*a + b) + b + 8 + 1
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axiom ex6 (a b : Nat) : 4 = 8 + a
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axiom ex7 (a b : Nat) : a + a ≤ 8 + a + a + b
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axiom ex8 (a b c d : Nat) : b + a + c + d ≤ a + b + a + b
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#eval test ``ex1
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#eval test ``ex2
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#eval test ``ex3
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#eval test ``ex4
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#eval test ``ex5
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#eval test ``ex6
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#eval test ``ex7
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#eval test ``ex8
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