@@ -503,10 +503,10 @@ Proof.
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case b; unfold Z.abs, Z.opp, Z.modulo, Z.div_eucl in |- *.
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auto with zarith.
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intros p q.
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- elim (Coq.ZArith. BinIntDef.Z.pos_div_eucl q (Zpos p)); intros Q R.
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+ elim (BinIntDef.Z.pos_div_eucl q (Zpos p)); intros Q R.
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intros Hlt Hp HR; rewrite HR; auto with zarith.
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intros p q.
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- elim (Coq.ZArith. BinIntDef.Z.pos_div_eucl q (Zpos p)); intros Q R.
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+ elim (BinIntDef.Z.pos_div_eucl q (Zpos p)); intros Q R.
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case R.
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auto with zarith.
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intro r'; intros H0 H1 H2.
@@ -518,10 +518,10 @@ Proof.
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case b; unfold Z.abs, Z.opp, Z.modulo, Z.div_eucl in |- *.
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auto with zarith.
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intros p q.
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- elim (Coq.ZArith. BinIntDef.Z.pos_div_eucl q (Zpos p)); intros Q R.
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+ elim (BinIntDef.Z.pos_div_eucl q (Zpos p)); intros Q R.
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case R; intros r' H0; intros; try (cut (Zpos r' = Zpos p); elim H0); auto with zarith.
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intros p q.
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- elim (Coq.ZArith. BinIntDef.Z.pos_div_eucl q (Zpos p)); intros Q R.
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+ elim (BinIntDef.Z.pos_div_eucl q (Zpos p)); intros Q R.
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case R; intros; try discriminate; try tauto.
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Qed .
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@@ -536,12 +536,12 @@ Proof.
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case b; unfold Z.opp in |- *.
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auto.
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intro B.
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- elim (Coq.ZArith. BinIntDef.Z.pos_div_eucl A (Zpos B)); intros q r.
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+ elim (BinIntDef.Z.pos_div_eucl A (Zpos B)); intros q r.
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intro Hr; rewrite Hr; auto.
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intro B.
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generalize (Z_mod_lt (Zpos A) (Zpos B)).
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unfold Z.modulo, Z.div_eucl in |- *.
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- elim (Coq.ZArith. BinIntDef.Z.pos_div_eucl A (Zpos B)); intros q r.
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+ elim (BinIntDef.Z.pos_div_eucl A (Zpos B)); intros q r.
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case r.
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intros _ HR; fold (- q)%Z in |- *; fold (- - q)%Z in |- *; rewrite Z.opp_involutive; auto.
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intros R Hlt HR.
@@ -558,7 +558,7 @@ Proof.
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intro B.
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generalize (Z_mod_lt (Zpos A) (Zpos B)).
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unfold Z.modulo, Z.div_eucl in |- *.
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- elim (Coq.ZArith. BinIntDef.Z.pos_div_eucl A (Zpos B)); intros q r.
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+ elim (BinIntDef.Z.pos_div_eucl A (Zpos B)); intros q r.
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case r.
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intros _ HR; fold (- q)%Z in |- *; fold (- - q)%Z in |- *; rewrite Z.opp_involutive; auto.
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intros R Hlt HR.
@@ -572,7 +572,7 @@ Proof.
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intro B.
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generalize (Z_mod_lt (Zpos A) (Zpos B)).
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unfold Z.modulo, Z.div_eucl in |- *.
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- elim (Coq.ZArith. BinIntDef.Z.pos_div_eucl A (Zpos B)); intros q r.
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+ elim (BinIntDef.Z.pos_div_eucl A (Zpos B)); intros q r.
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case r.
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intros _ HR; fold (- q)%Z in |- *; auto.
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intros; discriminate.
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