Nuprl Lemma : fpf-cap-subtype_functionality_wrt_sub
∀[A:Type]. ∀[d1,d2,d4:EqDecider(A)]. ∀[f,g:a:A fp-> Type]. ∀[x:A]. {g(x)?Top ⊆r f(x)?Top supposing f ⊆ g}
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
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-fpf2,
top_wf,
subtype_top,
fpf-sub_wf,
fpf_wf,
deq_wf,
subtype_rel_self,
fpf-cap_wf,
subtype_rel_wf,
fpf-cap_functionality_wrt_sub,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-dom_functionality2
\mforall{}[A:Type]. \mforall{}[d1,d2,d4:EqDecider(A)]. \mforall{}[f,g:a:A fp-> Type]. \mforall{}[x:A].
\{g(x)?Top \msubseteq{}r f(x)?Top supposing f \msubseteq{} g\}
Date html generated:
2015_07_17-AM-09_18_20
Last ObjectModification:
2015_01_28-AM-07_50_55
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