Nuprl Lemma : subtype-fpf-cap-top2
∀[X,T:Type]. ∀[eq:EqDecider(X)]. ∀[g:x:X fp-> Type]. ∀[x:X]. T ⊆r g(x)?Top supposing (↑x ∈ dom(g)) ⇒ (T ⊆r g(x))
Proof
Definitions occuring in Statement :
fpf-cap: f(x)?z,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
implies: P ⇒ Q,
universe: Type
Lemmas :
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
subtype_rel_wf,
fpf-ap_wf,
fpf_wf,
deq_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[X,T:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[g:x:X fp-> Type]. \mforall{}[x:X].
T \msubseteq{}r g(x)?Top supposing (\muparrow{}x \mmember{} dom(g)) {}\mRightarrow{} (T \msubseteq{}r g(x))
Date html generated:
2015_07_17-AM-09_17_54
Last ObjectModification:
2015_01_28-AM-07_50_37
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