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well_fnd
Nuprl Section: well_fnd

 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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