### Nuprl Lemma : fpf-sub-functionality2

[A,A':Type].
∀[B:A ─→ Type]. ∀[C:A' ─→ Type]. ∀[eq:EqDecider(A)]. ∀[eq':EqDecider(A')]. ∀[f,g:a:A fp-> B[a]].
(f ⊆ g) supposing (f ⊆ and (∀a:A. (B[a] ⊆C[a])))
supposing strong-subtype(A;A')

Proof

Definitions occuring in Statement :  fpf-sub: f ⊆ g fpf: a:A fp-> B[a] deq: EqDecider(T) strong-subtype: strong-subtype(A;B) uimplies: supposing a subtype_rel: A ⊆B uall: [x:A]. B[x] so_apply: x[s] all: x:A. B[x] function: x:A ─→ B[x] universe: Type
Lemmas :  fpf-dom_functionality2 subtype-fpf2 top_wf subtype_top strong-subtype-deq-subtype fpf-ap_wf equal_wf
\mforall{}[A,A':Type].
\mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[C:A'  {}\mrightarrow{}  Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[eq':EqDecider(A')].  \mforall{}[f,g:a:A  fp->  B[a]].
(f  \msubseteq{}  g)  supposing  (f  \msubseteq{}  g  and  (\mforall{}a:A.  (B[a]  \msubseteq{}r  C[a])))
supposing  strong-subtype(A;A')

Date html generated: 2015_07_17-AM-09_17_30
Last ObjectModification: 2015_01_28-AM-07_57_22

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