f40d72ea47
This PR adds draft typeclasses for `grind` to process facts about ordered modules. These interfaces will evolve as the implementation develops.
32 lines
1.1 KiB
Text
32 lines
1.1 KiB
Text
-- Tests for `grind` as a module normalization tactic, when only `NatModule`, `IntModule`, or `RatModule` is available.
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open Lean.Grind
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section NatModule
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variable (R : Type u) [NatModule R]
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example (a b : R) : a + b = b + a := by grind
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example (a : R) : a + 0 = a := by grind
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example (a : R) : 0 + a = a := by grind
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example (a b c : R) : a + b + c = a + (b + c) := by grind
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example (a : R) : 2 • a = a + a := by grind
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example (a b : R) : 2 • (b + c) = c + 2 • b + c := by grind
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end NatModule
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section IntModule
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variable (R : Type u) [IntModule R]
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example (a b : R) : a + b = b + a := by grind
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example (a : R) : a + 0 = a := by grind
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example (a : R) : 0 + a = a := by grind
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example (a b c : R) : a + b + c = a + (b + c) := by grind
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example (a : R) : 2 • a = a + a := by grind
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example (a : R) : (-2 : Int) • a = -a - a := by grind
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example (a b : R) : 2 • (b + c) = c + 2 • b + c := by grind
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example (a b c : R) : 2 • (b + c) - 3 • c + b + b = c + 5 • b - 2 • c := by grind
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example (a b c : R) : 2 • (b + c) + (-3 : Int) • c + b + b = c + (5 : Int) • b - 2 • c := by grind
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end IntModule
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