Nuprl Lemma : free-from-atom2-subtype
∀[A,B:Type]. ∀[x:A]. ∀[a:Atom2]. 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],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
free-from-atom_wf2,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
freeFromAtomApplication,
freeFromAtomTriviality,
Error :lambdaEquality_alt,
applyEquality,
Error :inhabitedIsType,
Error :universeIsType,
because_Cache,
atomnEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:A]. \mforall{}[a:Atom2]. a\#x:B supposing a\#x:A supposing A \msubseteq{}r B
Date html generated:
2019_06_20-AM-11_20_27
Last ObjectModification:
2018_09_27-PM-06_41_48
Theory : atom_1
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