Nuprl Lemma : fpf-null-domain
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:Void ⟶ Top]. (<[], f> = ⊗ ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-empty: ⊗,
fpf: a:A fp-> B[a],
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
function: x:A ⟶ B[x],
pair: <a, b>,
void: Void,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fpf-empty: ⊗,
fpf: a:A fp-> B[a],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
nil_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
l_member_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
functionExtensionality,
sqequalRule,
setElimination,
rename,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
setEquality,
functionEquality,
applyEquality,
voidEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:Void {}\mrightarrow{} Top]. (<[], f> = \motimes{})
Date html generated:
2018_05_21-PM-09_17_45
Last ObjectModification:
2018_02_09-AM-10_16_43
Theory : finite!partial!functions
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