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Author SHA1 Message Date
Kim Morrison
540d4a8abf chore: grind test file demonstrating interactive use 2026-01-23 04:46:54 +00:00

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import Lean.LibrarySuggestions.Default
theorem sq_inj (x y : Nat) (h : x ^ 2 = y ^ 2) : x = y := by
-- Puzzle for anyone bored: a quick Mathlib-free proof?
sorry
example (a b c d e : Nat) (_ : a = b) (_ : b = c) (_ : c ^ 2 = d ^ 2) (_ : d = e) : a = e := by
grind =>
-- We can verify that `grind` can see certain facts:
have : a = c
-- We can ask for all the known equivalence classes,
-- or classes involving certain terms:
show_eqcs a
-- We can add additional facts, giving proofs inline.
have : c = d := by grind? +suggestions
-- These facts are automatically used to extend equivalence classes,
-- so in this case the `have` statement itself closes the goal.
example (a b c d e : Nat) (_ : a = b) (_ : b = c) (_ : c ^ 2 = d ^ 2) (_ : d = e) : a = e := by
grind [sq_inj]
example (x y : Rat) (_ : x^2 = 1) (_ : x + y = 1) : y 2 := by
fail_if_success grind
grind =>
-- We can also use `have` statements as clues to guide `grind`.
have : x = 1 x = -1
-- Here `grind` can both prove the `have` statement (via a Grobner argument)
-- and finish off afterwards (using linear arithmetic),
-- even though it can't close the original goal by itself.
finish