Selected Objects

Introduction		Introductory Remarks
def	wellfounded	WellFnd{i}(A;x,y.R(x;y)) == P:(AProp). (j:A. (k:A. R(k;j)  P(k))  P(j))  {n:A. P(n)}
COM	INV_IMAGE_com	Inverse Image (Rank) Induction lemmas and tactics ...
THM	inv_image_ind_a	r:(TTProp), S:Type, f:(ST). WellFnd{i}(T;x,y.r(x,y))  WellFnd{i}(S;x,y.r(f(x),f(y)))
THM	inv_image_ind_tp	r:(TTProp), S:Type, f:(ST). WellFnd{i}(T;x,y.r(x,y))  WellFnd{i}(S;x,y.r(f(x),f(y)))
THM	inv_image_ind	r:(AAProp), B:Type, f:(BA). WellFnd{i}(A;x,y.r(x,y))  WellFnd{i}(B;x,y.r(f(x),f(y)))
COM	WFND_FUNCTIONALITY_tcom	Functionality lemmas for wellfounded predicate. ...
THM	wellfounded_functionality_wrt_implies	r1:(T1T1Prop), r2:(T2T2Prop). T1 = T2 (x,y:T1. r1(x,y)  r2(x,y)) WellFnd{i}(T1;x,y.r1(x,y))  WellFnd{i}(T2;x,y.r2(x,y))
THM	wellfounded_functionality_wrt_iff	r1:(T1T1Prop), r2:(T2T2Prop). T1 = T2 (x,y:T1. r1(x,y)  r2(x,y)) (WellFnd{i}(T1;x,y.r1(x,y))  WellFnd{i}(T2;x,y.r2(x,y)))

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