Nuprl Lemma : subtype_rel_function
∀[A,B,C,D:Type]. ((A ⟶ B) ⊆r (C ⟶ D)) supposing ((B ⊆r D) and (C ⊆r A))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
function: 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
Lemmas referenced :
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
functionExtensionality,
applyEquality,
hypothesisEquality,
thin,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
functionEquality,
axiomEquality,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B,C,D:Type]. ((A {}\mrightarrow{} B) \msubseteq{}r (C {}\mrightarrow{} D)) supposing ((B \msubseteq{}r D) and (C \msubseteq{}r A))
Date html generated:
2016_05_13-PM-03_18_38
Last ObjectModification:
2015_12_26-AM-09_08_25
Theory : subtype_0
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