Nuprl Lemma : free-from-atom-pair
∀[a:Atom1]. ∀[X,Y:Type]. ∀[x:X]. ∀[y:Y]. (a#<x, y>:X × Y) supposing (a#y:Y and a#x:X)
Proof
Definitions occuring in Statement :
free-from-atom: a#x:T,
atom: Atom$n,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pair: <a, b>,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
free-from-atom_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
freeFromAtomAxiom,
hypothesis,
sqequalRule,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
atomnEquality,
freeFromAtomApplication,
freeFromAtomTriviality,
lambdaEquality,
independent_pairEquality
Latex:
\mforall{}[a:Atom1]. \mforall{}[X,Y:Type]. \mforall{}[x:X]. \mforall{}[y:Y]. (a\#<x, y>:X \mtimes{} Y) supposing (a\#y:Y and a\#x:X)
Date html generated:
2016_05_13-PM-03_21_34
Last ObjectModification:
2015_12_26-AM-09_11_56
Theory : atom_1
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