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08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
31 lines
1.2 KiB
Lean4
31 lines
1.2 KiB
Lean4
import Lean.LibrarySuggestions.Default
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theorem sq_inj (x y : Nat) (h : x ^ 2 = y ^ 2) : x = y := by
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-- Puzzle for anyone bored: a quick Mathlib-free proof?
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sorry
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example (a b c d e : Nat) (_ : a = b) (_ : b = c) (_ : c ^ 2 = d ^ 2) (_ : d = e) : a = e := by
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grind =>
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-- We can verify that `grind` can see certain facts:
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have : a = c
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-- We can ask for all the known equivalence classes,
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-- or classes involving certain terms:
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show_eqcs a
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-- We can add additional facts, giving proofs inline.
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have : c = d := by grind? +suggestions
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-- These facts are automatically used to extend equivalence classes,
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-- so in this case the `have` statement itself closes the goal.
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example (a b c d e : Nat) (_ : a = b) (_ : b = c) (_ : c ^ 2 = d ^ 2) (_ : d = e) : a = e := by
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grind [sq_inj]
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example (x y : Rat) (_ : x^2 = 1) (_ : x + y = 1) : y ≤ 2 := by
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fail_if_success grind
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grind =>
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-- We can also use `have` statements as clues to guide `grind`.
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have : x = 1 ∨ x = -1
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-- Here `grind` can both prove the `have` statement (via a Grobner argument)
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-- and finish off afterwards (using linear arithmetic),
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-- even though it can't close the original goal by itself.
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finish
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