Nuprl Lemma : free-from-atom-l_member
∀[T:Type]. ∀[L:T List]. ∀[a:Atom1]. ∀[x:T]. (a#x:T) supposing (a#L:T List and (x ∈ L))
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
list: T List,
free-from-atom: a#x:T,
atom: Atom$n,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
prop: ℙ,
nat: ℕ,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
free-from-atom_wf,
list_wf,
l_member_wf,
less_than_wf,
length_wf,
nat_wf,
select_wf,
sq_stable__le,
set_wf,
free-from-atom-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
equalityElimination,
hypothesis,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
freeFromAtomAxiom,
isect_memberEquality,
because_Cache,
equalityTransitivity,
atomnEquality,
universeEquality,
dependent_set_memberEquality,
setElimination,
rename,
freeFromAtomApplication,
freeFromAtomTriviality,
lambdaEquality,
lambdaFormation,
independent_isectElimination,
natural_numberEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
freeFromAtomSet
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[a:Atom1]. \mforall{}[x:T]. (a\#x:T) supposing (a\#L:T List and (x \mmember{} L))
Date html generated:
2016_10_21-AM-09_48_32
Last ObjectModification:
2016_07_12-AM-05_08_32
Theory : list_0
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