Nuprl Lemma : fpf-is-empty_wf
∀[A:Type]. ∀[f:x:A fp-> Top]. (fpf-is-empty(f) ∈ 𝔹)
Proof
Definitions occuring in Statement :
fpf-is-empty: fpf-is-empty(f),
fpf: a:A fp-> B[a],
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fpf: a:A fp-> B[a],
fpf-is-empty: fpf-is-empty(f),
pi1: fst(t),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
eq_int_wf,
length_wf,
fpf_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:x:A fp-> Top]. (fpf-is-empty(f) \mmember{} \mBbbB{})
Date html generated:
2018_05_21-PM-09_17_40
Last ObjectModification:
2018_02_09-AM-10_16_41
Theory : finite!partial!functions
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