Nuprl Lemma : l_before_iseg
∀[T:Type]. ∀L1,L2:T List. ∀x,y:T. (L1 ≤ L2 ⇒ x before y ∈ L1 ⇒ x before y ∈ L2)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
l_before: x before y ∈ l,
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,
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
length_wf_nat,
equal_wf,
nat_wf,
sublist_transitivity,
cons_wf,
nil_wf,
sublist_append1,
sublist_wf,
exists_wf,
list_wf,
append_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
dependent_set_memberEquality,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
hyp_replacement,
Error :applyLambdaEquality,
setElimination,
rename,
lambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. \mforall{}x,y:T. (L1 \mleq{} L2 {}\mRightarrow{} x before y \mmember{} L1 {}\mRightarrow{} x before y \mmember{} L2)
Date html generated:
2016_10_21-AM-10_08_07
Last ObjectModification:
2016_07_12-AM-05_27_09
Theory : list_1
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