Nuprl Lemma : sub-family_transitivity
∀[P:Type]. ∀[F,G,H:P ⟶ Type]. (F ⊆ H) supposing (F ⊆ G and G ⊆ H)
Proof
Definitions occuring in Statement :
sub-family: F ⊆ G,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
sub-family: F ⊆ G,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
subtype_rel_transitivity,
all_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
lambdaEquality,
axiomEquality,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[P:Type]. \mforall{}[F,G,H:P {}\mrightarrow{} Type]. (F \msubseteq{} H) supposing (F \msubseteq{} G and G \msubseteq{} H)
Date html generated:
2016_05_14-AM-06_12_08
Last ObjectModification:
2015_12_26-PM-00_06_18
Theory : co-recursion
Home
Index