Nuprl Lemma : fpf-const-dom
∀[A:Type]. ∀eq:EqDecider(A). ∀L:A List. ∀v:Top. ∀x:A. (↑x ∈ dom(L |-fpf-> v) ⇐⇒ (x ∈ L))
Proof
Definitions occuring in Statement :
fpf-const: L |-fpf-> v,
fpf-dom: x ∈ dom(f),
l_member: (x ∈ l),
list: T List,
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
fpf-const: L |-fpf-> v,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
assert-deq-member,
assert_wf,
deq-member_wf,
assert_witness,
l_member_wf,
top_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
introduction,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}eq:EqDecider(A). \mforall{}L:A List. \mforall{}v:Top. \mforall{}x:A. (\muparrow{}x \mmember{} dom(L |-fpf-> v) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} L))
Date html generated:
2018_05_21-PM-09_24_19
Last ObjectModification:
2018_02_09-AM-10_19_47
Theory : finite!partial!functions
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