Nuprl Lemma : nil_before
∀[T:Type]. ∀x,y:T. (x before y ∈ [] ⇐⇒ False)
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
nil: [],
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
false: False,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
false: False,
l_before: x before y ∈ l,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
cons_sublist_nil,
cons_wf,
nil_wf,
l_before_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
voidElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}x,y:T. (x before y \mmember{} [] \mLeftarrow{}{}\mRightarrow{} False)
Date html generated:
2016_05_14-AM-07_45_16
Last ObjectModification:
2015_12_26-PM-02_53_13
Theory : list_1
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