Nuprl Lemma : non-void-decl_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[d:a:T fp-> Type]. (non-void(d) ∈ ℙ')
Proof
Definitions occuring in Statement :
non-void-decl: non-void(d),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
non-void-decl: non-void(d),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
so_apply: x[s1;s2]
Lemmas referenced :
fpf-all_wf,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaEquality,
universeEquality,
setEquality,
applyEquality,
hypothesis,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[d:a:T fp-> Type]. (non-void(d) \mmember{} \mBbbP{}')
Date html generated:
2018_05_21-PM-09_30_19
Last ObjectModification:
2018_02_09-AM-10_24_52
Theory : finite!partial!functions
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