Nuprl Lemma : concat_iseg
∀[T:Type]. ∀ll1,ll2:T List List. (ll1 ≤ ll2 ⇒ concat(ll1) ≤ concat(ll2))
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
concat: concat(ll),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
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],
top: Top
Lemmas referenced :
exists_wf,
list_wf,
equal_wf,
concat_wf,
append_wf,
concat_append
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaEquality,
universeEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_pairFormation,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}ll1,ll2:T List List. (ll1 \mleq{} ll2 {}\mRightarrow{} concat(ll1) \mleq{} concat(ll2))
Date html generated:
2016_10_21-AM-10_35_04
Last ObjectModification:
2016_07_12-AM-05_46_12
Theory : list_1
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