Nuprl Lemma : iseg_nil
∀[T:Type]. ∀L:T List. (L ≤ [] ⇐⇒ ↑null(L))
Proof
Definitions occuring in Statement :
iseg: 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 :
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
exists: ∃x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
true: True,
not: ¬A,
false: False
Lemmas referenced :
list_induction,
iff_wf,
list_wf,
equal-wf-base-T,
append_wf,
assert_wf,
null_wf,
list_ind_nil_lemma,
istype-void,
null_nil_lemma,
list_ind_cons_lemma,
null_cons_lemma,
nil_wf,
istype-assert,
decidable__true,
cons_wf,
decidable__false,
btrue_wf,
bfalse_wf,
btrue_neq_bfalse
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
Error :lambdaEquality_alt,
productEquality,
hypothesis,
baseClosed,
Error :universeIsType,
independent_functionElimination,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
rename,
Error :productIsType,
Error :functionIsType,
because_Cache,
Error :equalityIstype,
independent_pairFormation,
unionElimination,
natural_numberEquality,
Error :dependent_pairFormation_alt,
productElimination,
equalityTransitivity,
equalitySymmetry,
Error :dependent_set_memberEquality_alt,
Error :inhabitedIsType,
applyLambdaEquality,
setElimination
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. (L \mleq{} [] \mLeftarrow{}{}\mRightarrow{} \muparrow{}null(L))
Date html generated:
2019_06_20-PM-01_28_56
Last ObjectModification:
2019_01_10-PM-09_52_14
Theory : list_1
Home
Index