14 lines
485 B
Text
14 lines
485 B
Text
open eq eq.ops
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variable {A : Type}
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definition trans : Π {x y z : A} (p : x = y) (q : y = z), x = z
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| trans (refl a) (refl a) := refl a
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set_option pp.purify_locals false
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definition con_inv_cancel_left : Π {x y z : A} (p : x = y) (q : x = z), p ⬝ (p⁻¹ ⬝ q) = q
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| con_inv_cancel_left (refl a) (refl a) := refl (refl a)
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definition inv_con_cancel_left : Π {x y z : A} (p : x = y) (q : y = z), p⁻¹ ⬝ (p ⬝ q) = q
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| inv_con_cancel_left (refl a) (refl a) := refl (refl a)
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