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
Home
Index