Nuprl Lemma : fpf-empty_wf
∀[A:Type]. ∀[B:A ⟶ Type]. (⊗ ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-empty: ⊗,
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-empty: ⊗,
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
nil_wf,
it_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
setElimination,
rename,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
setEquality,
functionEquality,
axiomEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. (\motimes{} \mmember{} x:A fp-> B[x])
Date html generated:
2018_05_21-PM-09_17_38
Last ObjectModification:
2018_02_09-AM-10_16_37
Theory : finite!partial!functions
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