Nuprl Lemma : sublist_tl
∀[T:Type]. ∀L1,L2:T List. L1 ⊆ tl(L2) ⇒ L1 ⊆ L2 supposing ¬↑null(L2)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
null: null(as),
tl: tl(l),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s],
not: ¬A,
false: False,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
bfalse: ff,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q
Lemmas referenced :
list_induction,
all_wf,
list_wf,
isect_wf,
not_wf,
assert_wf,
null_wf,
sublist_wf,
tl_wf,
nil-sublist,
nil_wf,
cons_wf,
null_nil_lemma,
reduce_tl_nil_lemma,
true_wf,
null_cons_lemma,
reduce_tl_cons_lemma,
false_wf,
cons_sublist_cons,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
functionEquality,
independent_functionElimination,
dependent_functionElimination,
voidElimination,
rename,
isect_memberEquality,
voidEquality,
Error :universeIsType,
because_Cache,
universeEquality,
natural_numberEquality,
productElimination,
inrFormation,
productEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. L1 \msubseteq{} tl(L2) {}\mRightarrow{} L1 \msubseteq{} L2 supposing \mneg{}\muparrow{}null(L2)
Date html generated:
2019_06_20-PM-01_22_42
Last ObjectModification:
2018_09_26-PM-05_23_26
Theory : list_1
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