Nuprl Lemma : fpf-cap-join-subtype2
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> Type]. ∀[a:A]. f ⊕ g(a)?Top ⊆r g(a)?Top supposing f || g
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
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],
top: Top,
universe: Type
Lemmas :
fpf-join-cap-sq,
subtype-fpf2,
top_wf,
subtype_top,
fpf-compatible_wf,
fpf_wf,
deq_wf,
fpf-dom_wf,
bool_wf,
eqtt_to_assert,
subtype_rel-equal,
fpf-ap_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
subtype_rel_self,
fpf-cap_wf,
uiff_transitivity,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> Type]. \mforall{}[a:A].
f \moplus{} g(a)?Top \msubseteq{}r g(a)?Top supposing f || g
Date html generated:
2015_07_17-AM-11_13_47
Last ObjectModification:
2015_01_28-AM-07_42_37
Home
Index