Nuprl Lemma : l_disjoint_member
∀[T:Type]. ∀[l1,l2:T List]. ∀[x:T]. (¬(x ∈ l2)) supposing ((x ∈ l1) and l_disjoint(T;l1;l2))
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
l_disjoint: l_disjoint(T;l1;l2),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
all: ∀x:A. B[x],
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B
Lemmas referenced :
l_member_wf,
not_wf,
all_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
Error :universeIsType,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :inhabitedIsType,
productEquality,
universeEquality,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}[l1,l2:T List]. \mforall{}[x:T]. (\mneg{}(x \mmember{} l2)) supposing ((x \mmember{} l1) and l\_disjoint(T;l1;l2))
Date html generated:
2019_06_20-PM-01_26_57
Last ObjectModification:
2018_09_26-PM-05_37_07
Theory : list_1
Home
Index