lean4-htt/tests/lean/run/grind_ring_4.lean
Leonardo de Moura 0eb9671787
fix: proof term for Nullstellensatz certificate (#8168)
This PR fixes a bug when constructing the proof term for a
Nullstellensatz certificate produced by the new commutative ring
procedure in `grind`. The kernel was rejecting the proof term.
2025-04-30 01:03:57 +00:00

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open Lean.Grind
set_option grind.warning false
example {α} [CommRing α] [IsCharP α 0] [NoNatZeroDivisors α]
(d t : α)
(Δ40 : d + t + d * t = 0)
(Δ41 : 2 * d + 2 * d * t - 4 * d * t^2 + 2 * d * t^4 + 2 * d^2 * t^4 = 0) :
t + 2 * t^2 - t^3 - 2 * t^4 + t^5 = 0 := by
grind +ring
example {α} [CommRing α] [IsCharP α 0] [NoNatZeroDivisors α]
(d t d_inv : α)
(Δ40 : d * (d + t + d * t) = 0)
(Δ41 : d^2 * (d + d * t - 2 * d * t^2 + d * t^4 + d^2 * t^4) = 0)
(_ : d * d_inv = 1) :
t + 2 * t^2 - t^3 - 2 * t^4 + t^5 = 0 := by
grind +ring