src/FOLP/ex/Foundation.thy
 author wenzelm Fri, 23 Apr 2010 23:35:43 +0200 changeset 36319 8feb2c4bef1a parent 35762 af3ff2ba4c54 child 41526 54b4686704af permissions -rw-r--r--
mark schematic statements explicitly;
```
(*  Title:      FOLP/ex/Foundation.ML
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
*)

header "Intuitionistic FOL: Examples from The Foundation of a Generic Theorem Prover"

theory Foundation
imports IFOLP
begin

schematic_lemma "?p : A&B  --> (C-->A&C)"
apply (rule impI)
apply (rule impI)
apply (rule conjI)
prefer 2 apply assumption
apply (rule conjunct1)
apply assumption
done

text {*A form of conj-elimination*}
schematic_lemma
assumes "p : A & B"
and "!!x y. x : A ==> y : B ==> f(x, y) : C"
shows "?p : C"
apply (rule prems)
apply (rule conjunct1)
apply (rule prems)
apply (rule conjunct2)
apply (rule prems)
done

schematic_lemma
assumes "!!A x. x : ~ ~A ==> cla(x) : A"
shows "?p : B | ~B"
apply (rule prems)
apply (rule notI)
apply (rule_tac P = "~B" in notE)
apply (rule_tac [2] notI)
apply (rule_tac [2] P = "B | ~B" in notE)
prefer 2 apply assumption
apply (rule_tac [2] disjI1)
prefer 2 apply assumption
apply (rule notI)
apply (rule_tac P = "B | ~B" in notE)
apply assumption
apply (rule disjI2)
apply assumption
done

schematic_lemma
assumes "!!A x. x : ~ ~A ==> cla(x) : A"
shows "?p : B | ~B"
apply (rule prems)
apply (rule notI)
apply (rule notE)
apply (rule_tac [2] notI)
apply (erule_tac [2] notE)
apply (erule_tac [2] disjI1)
apply (rule notI)
apply (erule notE)
apply (erule disjI2)
done

schematic_lemma
assumes "p : A | ~A"
and "q : ~ ~A"
shows "?p : A"
apply (rule disjE)
apply (rule prems)
apply assumption
apply (rule FalseE)
apply (rule_tac P = "~A" in notE)
apply (rule prems)
apply assumption
done

subsection "Examples with quantifiers"

schematic_lemma
assumes "p : ALL z. G(z)"
shows "?p : ALL z. G(z)|H(z)"
apply (rule allI)
apply (rule disjI1)
apply (rule prems [THEN spec])
done

schematic_lemma "?p : ALL x. EX y. x=y"
apply (rule allI)
apply (rule exI)
apply (rule refl)
done

schematic_lemma "?p : EX y. ALL x. x=y"
apply (rule exI)
apply (rule allI)
apply (rule refl)?
oops

text {* Parallel lifting example. *}
schematic_lemma "?p : EX u. ALL x. EX v. ALL y. EX w. P(u,x,v,y,w)"
apply (rule exI allI)
apply (rule exI allI)
apply (rule exI allI)
apply (rule exI allI)
apply (rule exI allI)
oops

schematic_lemma
assumes "p : (EX z. F(z)) & B"
shows "?p : EX z. F(z) & B"
apply (rule conjE)
apply (rule prems)
apply (rule exE)
apply assumption
apply (rule exI)
apply (rule conjI)
apply assumption
apply assumption
done

text {* A bigger demonstration of quantifiers -- not in the paper. *}
schematic_lemma "?p : (EX y. ALL x. Q(x,y)) -->  (ALL x. EX y. Q(x,y))"
apply (rule impI)
apply (rule allI)
apply (rule exE, assumption)
apply (rule exI)
apply (rule allE, assumption)
apply assumption
done

end
```