Nuprl Lemma : sub-family_wf
∀[P:Type]. ∀[F,G:P ⟶ Type]. (F ⊆ G ∈ ℙ)
Proof
Definitions occuring in Statement :
sub-family: F ⊆ G,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sub-family: F ⊆ G,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[P:Type]. \mforall{}[F,G:P {}\mrightarrow{} Type]. (F \msubseteq{} G \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_12_08
Last ObjectModification:
2015_12_26-PM-00_06_16
Theory : co-recursion
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