Nuprl Lemma : req_functionality

[x1,x2,y1,y2:ℝ].  (uiff(x1 y1;x2 y2)) supposing ((y1 y2) and (x1 x2))


Definitions occuring in Statement :  req: y real: uiff: uiff(P;Q) uimplies: supposing a uall: [x:A]. B[x]
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a uiff: uiff(P;Q) and: P ∧ Q equiv_rel: EquivRel(T;x,y.E[x; y]) implies:  Q prop: trans: Trans(T;x,y.E[x; y]) all: x:A. B[x] guard: {T} sym: Sym(T;x,y.E[x; y])
Lemmas referenced :  req-equiv req_witness req_wf real_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation lemma_by_obid sqequalHypSubstitution productElimination thin isectElimination hypothesisEquality independent_functionElimination hypothesis sqequalRule independent_pairEquality isect_memberEquality because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination

\mforall{}[x1,x2,y1,y2:\mBbbR{}].    (uiff(x1  =  y1;x2  =  y2))  supposing  ((y1  =  y2)  and  (x1  =  x2))

Date html generated: 2016_05_18-AM-06_50_36
Last ObjectModification: 2015_12_28-AM-00_29_18

Theory : reals

Home Index