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Diffstat (limited to 'theories/Ints/BigZ.v')
| -rw-r--r-- | theories/Ints/BigZ.v | 48 |
1 files changed, 0 insertions, 48 deletions
diff --git a/theories/Ints/BigZ.v b/theories/Ints/BigZ.v deleted file mode 100644 index 8c7c1f809c..0000000000 --- a/theories/Ints/BigZ.v +++ /dev/null @@ -1,48 +0,0 @@ -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. - |
