Nuprl Lemma : free-from-atom-subtype
∀[A,B:Type]. ∀[x:A]. ∀[a:Atom1]. a#x:B supposing a#x:A supposing A ⊆r B
Proof
Definitions occuring in Statement :
free-from-atom: a#x:T,
atom: Atom$n,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
free-from-atom_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
freeFromAtomApplication,
freeFromAtomTriviality,
lambdaEquality,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalHypSubstitution,
freeFromAtomAxiom,
extract_by_obid,
isectElimination,
thin,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
atomnEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:A]. \mforall{}[a:Atom1]. a\#x:B supposing a\#x:A supposing A \msubseteq{}r B
Date html generated:
2019_06_20-AM-11_20_26
Last ObjectModification:
2018_09_14-AM-10_41_36
Theory : atom_1
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