Nuprl Lemma : iseg-sorted-by
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀sa,sb:T List. (sa ≤ sb ⇒ sorted-by(R;sb) ⇒ sorted-by(R;sa))
Proof
Definitions occuring in Statement :
sorted-by: sorted-by(R;L),
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
sublist-sorted-by,
iseg_wf,
list_wf,
sublist_iseg
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}sa,sb:T List. (sa \mleq{} sb {}\mRightarrow{} sorted-by(R;sb) {}\mRightarrow{} sorted-by(R;sa))
Date html generated:
2016_05_14-PM-01_48_18
Last ObjectModification:
2015_12_26-PM-05_34_57
Theory : list_1
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