Nuprl Lemma : fseg_nil
∀[T:Type]. ∀L:T List. (fseg(T;L;[]) ⇐⇒ ↑null(L))
Proof
Definitions occuring in Statement :
fseg: fseg(T;L1;L2),
null: null(as),
nil: [],
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
fseg: fseg(T;L1;L2),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
top: Top,
bfalse: ff,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
true: True,
not: ¬A,
false: False,
exists: ∃x:A. B[x],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
uiff: uiff(P;Q),
uimplies: b supposing a
Lemmas referenced :
list_induction,
iff_wf,
exists_wf,
list_wf,
equal-wf-base-T,
assert_wf,
null_wf,
null_nil_lemma,
null_cons_lemma,
append_wf,
decidable__true,
nil_wf,
list_ind_nil_lemma,
cons_wf,
false_wf,
decidable__false,
btrue_wf,
append_is_nil,
and_wf,
equal_wf,
bfalse_wf,
btrue_neq_bfalse
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
lambdaEquality,
hypothesis,
because_Cache,
independent_functionElimination,
rename,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
baseClosed,
independent_pairFormation,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
productElimination,
equalitySymmetry,
independent_isectElimination,
dependent_set_memberEquality,
equalityTransitivity,
applyLambdaEquality,
setElimination,
addLevel,
levelHypothesis
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. (fseg(T;L;[]) \mLeftarrow{}{}\mRightarrow{} \muparrow{}null(L))
Date html generated:
2018_05_21-PM-06_30_24
Last ObjectModification:
2018_05_19-PM-04_40_56
Theory : general
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