4500a7f02b
This PR removes the `NatCast (Fin n)` global instance (both the direct instance, and the indirect one via `Lean.Grind.Semiring`), as that instance causes causes `x < n` (for `x : Fin k`, `n : Nat`) to be elaborated as `x < ↑n` rather than `↑x < n`, which is undesirable. Note however that in Mathlib this happens anyway!
30 lines
641 B
Text
30 lines
641 B
Text
set_option pp.mvars false
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-- We first verify that there is no global coercion from `Nat` to `Fin n`.
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-- Such a coercion would frequently introduce unexpected modular arithmetic.
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/--
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error: type mismatch
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n
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has type
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Nat : Type
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but is expected to have type
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Fin 3 : Type
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---
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info: fun n => sorry : (n : Nat) → ?_ n
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-/
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#guard_msgs in #check fun (n : Nat) => (n : Fin 3)
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-- This instance is available via `open Fin.NatCast in ...`
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section
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open Fin.NatCast
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variable (m : Nat) (n : Fin 3)
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/-- info: n < ↑m : Prop -/
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#guard_msgs in #check n < m
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end
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example (x : Fin (n + 1)) (h : x < n) : Fin (n + 1) := x.succ.castLT (by simp [h])
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