Nuprl Lemma : append-impossible
∀[T:Type]. ∀[as,bs:T List]. ∀[b:T]. uiff(as = (as @ [b / bs]) ∈ (T List);False)
Proof
Definitions occuring in Statement :
append: as @ bs,
cons: [a / b],
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
false: False,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
list_wf,
append_wf,
cons_wf,
false_wf,
append-nil,
subtype_rel_list,
top_wf,
nil_wf,
length_wf,
null_nil_lemma,
btrue_wf,
and_wf,
null_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
append-cancellation
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
because_Cache,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
voidElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
universeEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
voidEquality,
dependent_set_memberEquality,
setElimination,
rename,
setEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. \mforall{}[b:T]. uiff(as = (as @ [b / bs]);False)
Date html generated:
2016_05_14-AM-07_39_22
Last ObjectModification:
2015_12_26-PM-02_13_14
Theory : list_1
Home
Index