KeenS

$ cim for alisp ccl clisp ecl gcl sbcl do -qe '(print (expt 1.01 365))'
>>>alisp -qe (print (expt 1.01 365))

37.783386 ; Exiting
<<<
>>>ccl -qe (print (expt 1.01 365))

37.783386 
<<<
>>>clisp -qe (print (expt 1.01 365))

KeenS

range
datetime (date & time)
set
sortedset
queue
tree (btree)
regexp
format scanner
lazy
copy

KeenS

Theorem Modus_ponens : forall P Q : Prop, P -> (P -> Q) -> Q.
Proof.
  intros.
  apply H0.
  assumption.
Qed.

KeenS

Theorem Modus_tollens : forall P Q : Prop, ~Q /\ (P -> Q) -> ~P.
Proof.
  intros.
  destruct H.
  intro.
  apply H.
  apply H0.
  apply H1.
Qed.

KeenS

Theorem Disjunctive_syllogism : forall P Q : Prop, (P \/ Q) -> ~P -> Q.
Proof.
  intros.
  destruct H.
  destruct H0.
  apply H.
  apply H.
Qed.

KeenS

Theorem DeBolran1 : forall P Q : Prop, ~P \/ ~Q -> ~(P /\ Q).
Proof.
  intros.
  destruct H.
  intro.
  destruct H0.
  apply H, H0.
  intro.
  destruct H.
  destruct H0.

KeenS

Lemma NotNot : forall P : Prop, P -> ~~P.
Proof.
  intros.
  unfold not.
  intros.
  apply H0.
  apply H.
Qed.

Require Import Classical.

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Theorem DeMorgan3 : forall P Q : Prop, ~(P \/ Q) -> ~P /\ ~Q.
Proof.
  intros.
  split.
  intro.
  destruct H.
  left.
  apply H0.
  intro.
  destruct H.

KeenS

Require Import Arith.

Goal forall x y, x < y -> x + 10 < y + 10.
Proof.
  intros.
  apply plus_lt_compat_r.
  apply H.
Qed.

KeenS

Goal forall P Q : nat -> Prop, P 0 -> (forall x , P x -> Q x) -> Q 0.
Proof.
  intros.
  apply H0.
  apply H.
Qed.

Goal forall P : nat -> Prop, P 2 -> (exists y, P (1 + y)).
Proof.
  intros.