Nuprl Lemma : singleton_before
∀[T:Type]. ∀a,x,y:T. (x before y ∈ [a] ⇐⇒ False)
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
cons: [a / b],
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],
l_before: x before y ∈ l,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
false: False,
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
guard: {T}
Lemmas referenced :
or_wf,
equal_wf,
false_wf,
cons_sublist_nil,
nil_wf,
cons_wf,
sublist_wf,
iff_wf,
cons_sublist_cons
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
independent_pairFormation,
sqequalHypSubstitution,
unionElimination,
thin,
productElimination,
voidElimination,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
productEquality,
hypothesisEquality,
addLevel,
independent_functionElimination,
inlFormation,
because_Cache,
dependent_functionElimination,
sqequalRule,
inrFormation,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}a,x,y:T. (x before y \mmember{} [a] \mLeftarrow{}{}\mRightarrow{} False)
Date html generated:
2019_06_20-PM-01_23_15
Last ObjectModification:
2018_08_24-PM-11_30_00
Theory : list_1
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