Nuprl Lemma : fpf-cap-subtype_functionality_wrt_sub2
∀[A1,A2,A3:Type]. ∀[d,d':EqDecider(A3)]. ∀[d2:EqDecider(A2)]. ∀[f:a:A1 fp-> Type]. ∀[g:a:A2 fp-> Type]. ∀[x:A3].
({g(x)?Top ⊆r f(x)?Top supposing f ⊆ g}) supposing (strong-subtype(A2;A3) and strong-subtype(A1;A2))
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
guard: {T},
universe: Type
Lemmas :
decidable__assert,
fpf-dom_wf,
subtype-fpf3,
top_wf,
subtype_top,
subtype_rel_self,
fpf-cap_wf,
subtype_rel_wf,
fpf-cap_functionality_wrt_sub,
assert_wf,
fpf-dom-type2,
subtype-fpf2,
fpf-dom_functionality2,
strong-subtype-deq-subtype,
bool_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A1,A2,A3:Type]. \mforall{}[d,d':EqDecider(A3)]. \mforall{}[d2:EqDecider(A2)]. \mforall{}[f:a:A1 fp-> Type].
\mforall{}[g:a:A2 fp-> Type]. \mforall{}[x:A3].
(\{g(x)?Top \msubseteq{}r f(x)?Top supposing f \msubseteq{} g\}) supposing
(strong-subtype(A2;A3) and
strong-subtype(A1;A2))
Date html generated:
2015_07_17-AM-09_18_25
Last ObjectModification:
2015_01_28-AM-07_58_43
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