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-rw-r--r--theories/Ints/BigZ.v48
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diff --git a/theories/Ints/BigZ.v b/theories/Ints/BigZ.v
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-Require Export BigN.
-Require Import ZMake.
-
-
-Module BigZ := Make BigN.
-
-
-Definition bigZ := BigZ.t.
-
-Delimit Scope bigZ_scope with bigZ.
-Bind Scope bigZ_scope with bigZ.
-Bind Scope bigZ_scope with BigZ.t.
-Bind Scope bigZ_scope with BigZ.t_.
-
-Notation " i + j " := (BigZ.add i j) : bigZ_scope.
-Notation " i - j " := (BigZ.sub i j) : bigZ_scope.
-Notation " i * j " := (BigZ.mul i j) : bigZ_scope.
-Notation " i / j " := (BigZ.div i j) : bigZ_scope.
-Notation " i ?= j " := (BigZ.compare i j) : bigZ_scope.
-
-
- Theorem spec_to_Z:
- forall n, BigN.to_Z (BigZ.to_N n) =
- (Zsgn (BigZ.to_Z n) * BigZ.to_Z n)%Z.
- intros n; case n; simpl; intros p;
- generalize (BigN.spec_pos p); case (BigN.to_Z p); auto.
- intros p1 H1; case H1; auto.
- intros p1 H1; case H1; auto.
- Qed.
-
- Theorem spec_to_N n:
- (BigZ.to_Z n =
- Zsgn (BigZ.to_Z n) * (BigN.to_Z (BigZ.to_N n)))%Z.
- intros n; case n; simpl; intros p;
- generalize (BigN.spec_pos p); case (BigN.to_Z p); auto.
- intros p1 H1; case H1; auto.
- intros p1 H1; case H1; auto.
- Qed.
-
- Theorem spec_to_Z_pos:
- forall n, (0 <= BigZ.to_Z n ->
- BigN.to_Z (BigZ.to_N n) = BigZ.to_Z n)%Z.
- intros n; case n; simpl; intros p;
- generalize (BigN.spec_pos p); case (BigN.to_Z p); auto.
- intros p1 _ H1; case H1; auto.
- intros p1 H1; case H1; auto.
- Qed.
-