Nuprl Lemma : compat-iseg2
∀[T:Type]. ∀L1,L2,L3:T List. (L1 ≤ L2 ⇒ L3 || L2 ⇒ L3 || L1)
Proof
Definitions occuring in Statement :
compat: l1 || l2,
iseg: l1 ≤ l2,
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,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
compat_symmetry,
compat-iseg,
compat_wf,
iseg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
because_Cache,
hypothesis,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2,L3:T List. (L1 \mleq{} L2 {}\mRightarrow{} L3 || L2 {}\mRightarrow{} L3 || L1)
Date html generated:
2016_05_15-PM-03_50_23
Last ObjectModification:
2015_12_27-PM-01_23_12
Theory : general
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