Nuprl Lemma : fpf-empty-compatible-left
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:Top]. ∀[f:a:A fp-> Top]. ⊗ || f
Proof
Definitions occuring in Statement :
fpf-compatible: f || g,
fpf-empty: ⊗,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
universe: Type
Definitions unfolded in proof :
fpf-compatible: f || g,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
fpf-empty: ⊗,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
deq_member_nil_lemma,
and_wf,
assert_wf,
fpf-dom_wf,
fpf-empty_wf,
top_wf,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
hypothesisEquality,
lambdaEquality,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:Top]. \mforall{}[f:a:A fp-> Top]. \motimes{} || f
Date html generated:
2018_05_21-PM-09_30_37
Last ObjectModification:
2018_02_09-AM-10_25_09
Theory : finite!partial!functions
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