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
Lemmas :
subtype_rel_tagged+_general,
tagged+_wf,
isect2_subtype_rel3,
tag-case_wf,
subtype_rel-tag-case,
subtype_rel_wf,
Id_wf,
unit_wf2,
isect2_subtype_rel2,
all_wf
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:
2015_07_23-AM-11_06_36
Last ObjectModification:
2015_01_29-AM-00_11_18
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