Nuprl Lemma : subtype-fpf-cap-void2
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[f,g:x:X fp-> Type]. ∀[x:X]. ∀[z:g(x)?Void]. f(x)?Void ⊆r g(x)?Void supposing f || g
Proof
Definitions occuring in Statement :
fpf-compatible: 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],
void: Void,
universe: Type
Lemmas :
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-ap_wf,
iff_weakening_equal,
subtype_rel_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[f,g:x:X fp-> Type]. \mforall{}[x:X]. \mforall{}[z:g(x)?Void].
f(x)?Void \msubseteq{}r g(x)?Void supposing f || g
Date html generated:
2015_07_17-AM-09_18_48
Last ObjectModification:
2015_02_04-PM-05_07_05
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