Nuprl Lemma : subtype-fpf-cap-void-list
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[f,g:x:X fp-> Type]. ∀[x:X]. (f(x)?Void List) ⊆r (g(x)?Void List) supposing f ⊆ g
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
list: T List,
deq: EqDecider(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
void: Void,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
subtype_rel_list,
fpf-cap_wf,
subtype-fpf-cap-void,
fpf-sub_wf,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
universeEquality,
voidEquality,
hypothesis,
independent_isectElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[f,g:x:X fp-> Type]. \mforall{}[x:X].
(f(x)?Void List) \msubseteq{}r (g(x)?Void List) supposing f \msubseteq{} g
Date html generated:
2018_05_21-PM-09_20_48
Last ObjectModification:
2018_02_09-AM-10_17_58
Theory : finite!partial!functions
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