de493d761d
This PR upstreams the definition of Rat from Batteries, for use in our planned interval arithmetic tactic. --------- Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
26 lines
584 B
Text
26 lines
584 B
Text
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/-!
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Test the `rightact%` elaborator for `HPow.hPow`, added to address #2854
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-/
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open Lean
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variable (n : Nat) (m : Int) (q : Rat)
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#check n ^ 2 + m ^ 2
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#check n ^ 2 + 1
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#check (n ^ 2 + 1 : Int)
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#check (n ^ 2 + (1 : Nat) : Int)
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instance instNatPowRat : NatPow Rat where
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pow q n := mkRat (q.num ^ n) (q.den ^ n)
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instance instPowRatInt : Pow Rat Int where
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pow q m := if 0 ≤ m then q ^ (m.toNat : Nat) else (1/q) ^ ((-m).toNat)
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#check q ^ n + 1
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#check q ^ m + 1
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#check q ^ (n : Int) + 1
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#check 12 * q + 1 ≤ 13 * q ^ 2
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#check (12 : Rat) * q + (1 : Rat) ≤ (13 : Rat) * q ^ 2
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