Nuprl Lemma : Com-subtype
∀[M:Type ⟶ Type]
∀[A,B:Type]. (Com(P.M[P]) A) ⊆r (Com(P.M[P]) B) supposing A ⊆r B supposing ∀A,B:Type. ((A ⊆r B) ⇒ (M[A] ⊆r M[B]))
Proof
Definitions occuring in Statement :
Com: Com(P.M[P]),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
Com: Com(P.M[P]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x]
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[A,B:Type]. (Com(P.M[P]) A) \msubseteq{}r (Com(P.M[P]) B) supposing A \msubseteq{}r B
supposing \mforall{}A,B:Type. ((A \msubseteq{}r B) {}\mRightarrow{} (M[A] \msubseteq{}r M[B]))
Date html generated:
2016_05_17-AM-10_22_13
Last ObjectModification:
2015_12_29-PM-05_28_35
Theory : process-model
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