Fix definition of 'less than' to not involve a third variable.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@@ -30,14 +30,14 @@ private
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⊥ᴬ≼ a with ≈-dec a ⊥ᴬ
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... | yes a≈⊥ᴬ = ≼-cong a≈⊥ᴬ ≈-refl (≼-refl a)
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... | no a̷≈⊥ᴬ with ≈-dec ⊥ᴬ (a ⊓ ⊥ᴬ)
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... | yes ⊥ᴬ≈a⊓⊥ᴬ = (a , ≈-trans (⊔-comm ⊥ᴬ a) (≈-trans (≈-⊔-cong (≈-refl {a}) ⊥ᴬ≈a⊓⊥ᴬ) (absorb-⊔-⊓ a ⊥ᴬ)))
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... | yes ⊥ᴬ≈a⊓⊥ᴬ = ≈-trans (⊔-comm ⊥ᴬ a) (≈-trans (≈-⊔-cong (≈-refl {a}) ⊥ᴬ≈a⊓⊥ᴬ) (absorb-⊔-⊓ a ⊥ᴬ))
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... | no ⊥ᴬ̷≈a⊓⊥ᴬ = ⊥-elim (ChainA.Bounded-suc-n (proj₂ fixedHeight) (ChainA.step x≺⊥ᴬ ≈-refl (proj₂ (proj₁ fixedHeight))))
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where
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⊥ᴬ⊓a̷≈⊥ᴬ : ¬ (⊥ᴬ ⊓ a) ≈ ⊥ᴬ
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⊥ᴬ⊓a̷≈⊥ᴬ = λ ⊥ᴬ⊓a≈⊥ᴬ → ⊥ᴬ̷≈a⊓⊥ᴬ (≈-trans (≈-sym ⊥ᴬ⊓a≈⊥ᴬ) (⊓-comm _ _))
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x≺⊥ᴬ : (⊥ᴬ ⊓ a) ≺ ⊥ᴬ
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x≺⊥ᴬ = ((⊥ᴬ , ≈-trans (⊔-comm _ _) (≈-trans (≈-refl {⊥ᴬ ⊔ (⊥ᴬ ⊓ a)}) (absorb-⊔-⊓ ⊥ᴬ a))) , ⊥ᴬ⊓a̷≈⊥ᴬ)
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x≺⊥ᴬ = (≈-trans (⊔-comm _ _) (≈-trans (≈-refl {⊥ᴬ ⊔ (⊥ᴬ ⊓ a)}) (absorb-⊔-⊓ ⊥ᴬ a)) , ⊥ᴬ⊓a̷≈⊥ᴬ)
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-- using 'g', for gas, here helps make sure the function terminates.
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-- since A forms a fixed-height lattice, we must find a solution after
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