Nuprl Lemma : fpf-sub_transitivity
∀[A:Type]. ∀[B:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[f,g,h:a:A fp-> B[a]]. (f ⊆ h) supposing (g ⊆ h and f ⊆ g)
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert_elim,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_wf,
fpf-sub_witness,
fpf-sub_wf,
fpf_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g,h:a:A fp-> B[a]].
(f \msubseteq{} h) supposing (g \msubseteq{} h and f \msubseteq{} g)
Date html generated:
2015_07_17-AM-09_17_37
Last ObjectModification:
2015_01_28-AM-07_51_43
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