Nuprl Lemma : append_is_nil
∀[T:Type]. ∀[l1,l2:T List]. uiff((l1 @ l2) = [] ∈ (T List);(l1 = [] ∈ (T List)) ∧ (l2 = [] ∈ (T List)))
Proof
Definitions occuring in Statement :
append: as @ bs,
nil: [],
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
not: ¬A,
false: False
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
uiff_wf,
equal_wf,
append_wf,
nil_wf,
and_wf,
list_ind_nil_lemma,
list_ind_cons_lemma,
null_nil_lemma,
btrue_wf,
null_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
cons_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairEquality,
axiomEquality,
because_Cache,
lambdaFormation,
rename,
dependent_set_memberEquality,
applyEquality,
setElimination,
setEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l1,l2:T List]. uiff((l1 @ l2) = [];(l1 = []) \mwedge{} (l2 = []))
Date html generated:
2016_05_14-AM-06_42_12
Last ObjectModification:
2015_12_26-PM-00_29_32
Theory : list_0
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