Nuprl Lemma : l_before_append
∀[T:Type]. ∀L1,L2:T List. ∀x,y:T. ((x ∈ L1) ⇒ (y ∈ L2) ⇒ x before y ∈ L1 @ L2)
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
l_member: (x ∈ l),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
l_before: x before y ∈ l,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
l_member_wf,
list_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
sublist_append,
cons_wf,
nil_wf,
member_iff_sublist
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :universeIsType,
universeEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
independent_functionElimination,
productElimination
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. \mforall{}x,y:T. ((x \mmember{} L1) {}\mRightarrow{} (y \mmember{} L2) {}\mRightarrow{} x before y \mmember{} L1 @ L2)
Date html generated:
2019_06_20-PM-01_23_20
Last ObjectModification:
2018_09_26-PM-05_27_53
Theory : list_1
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