Nuprl Lemma : iseg_single
∀[T:Type]. ∀L:T List. ∀x:T. (L ≤ [x] ⇐⇒ (↑null(L)) ∨ (L = [x] ∈ (T List)))
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
null: null(as),
cons: [a / b],
nil: [],
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q
Lemmas referenced :
iseg_append_single,
nil_wf,
list_ind_nil_lemma,
or_wf,
assert_wf,
null_wf,
equal_wf,
list_wf,
cons_wf,
iseg_nil,
iseg_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
independent_pairFormation,
addLevel,
independent_functionElimination,
orFunctionality,
impliesFunctionality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}x:T. (L \mleq{} [x] \mLeftarrow{}{}\mRightarrow{} (\muparrow{}null(L)) \mvee{} (L = [x]))
Date html generated:
2016_05_14-PM-03_02_51
Last ObjectModification:
2015_12_26-PM-01_55_40
Theory : list_1
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