### Nuprl Lemma : req_functionality

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

Proof

Definitions occuring in Statement :  req: `x = y` real: `ℝ` uiff: `uiff(P;Q)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` uiff: `uiff(P;Q)` and: `P ∧ Q` equiv_rel: `EquivRel(T;x,y.E[x; y])` implies: `P `` Q` prop: `ℙ` 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

Latex:
\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

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