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+Require Import Int63.
+
+Set Implicit Arguments.
+
+Open Scope int63_scope.
+
+Check (eq_refl : tail0 2305843009213693952 = 61).
+Check (eq_refl 61 <: tail0 2305843009213693952 = 61).
+Check (eq_refl 61 <<: tail0 2305843009213693952 = 61).
+Definition compute1 := Eval compute in tail0 2305843009213693952.
+Check (eq_refl compute1 : 61 = 61).
+
+Check (eq_refl : tail0 1 = 0).
+Check (eq_refl 0 <: tail0 1 = 0).
+Check (eq_refl 0 <<: tail0 1 = 0).
+Definition compute2 := Eval compute in tail0 1.
+Check (eq_refl compute2 : 0 = 0).
+
+Check (eq_refl : tail0 0 = 63).
+Check (eq_refl 63 <: tail0 0 = 63).
+Check (eq_refl 63 <<: tail0 0 = 63).
+Definition compute3 := Eval compute in tail0 0.
+Check (eq_refl compute3 : 63 = 63).