Nuprl Lemma : fseg_member
∀[T:Type]. ∀l1,l2:T List. ∀x:T. (fseg(T;l1;l2) ⇒ (x ∈ l1) ⇒ (x ∈ l2))
Proof
Definitions occuring in Statement :
fseg: fseg(T;L1;L2),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
fseg: fseg(T;L1;L2),
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q
Lemmas referenced :
length_wf_nat,
equal_wf,
nat_wf,
member_append,
l_member_wf,
fseg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
dependent_set_memberEquality,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
inrFormation,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
setElimination,
rename,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. \mforall{}x:T. (fseg(T;l1;l2) {}\mRightarrow{} (x \mmember{} l1) {}\mRightarrow{} (x \mmember{} l2))
Date html generated:
2016_10_25-AM-10_45_32
Last ObjectModification:
2016_07_12-AM-06_54_56
Theory : general
Home
Index