Nuprl Lemma : assert-int-list-member
∀i:ℤ. ∀xs:ℤ List. (↑int-list-member(i;xs) ⇐⇒ (i ∈ xs))
Proof
Definitions occuring in Statement :
int-list-member: int-list-member(i;xs),
l_member: (x ∈ l),
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
int-list-member: int-list-member(i;xs),
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
false: False,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
not: ¬A,
or: P ∨ Q,
guard: {T},
subtype_rel: A ⊆r B,
uiff: uiff(P;Q)
Lemmas referenced :
list_induction,
iff_wf,
assert_wf,
int-list-member_wf,
l_member_wf,
list_wf,
reduce_nil_lemma,
reduce_cons_lemma,
false_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
equal-wf-base,
or_wf,
int_subtype_base,
cons_member,
cons_wf,
bor_wf,
eq_int_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bor,
assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
rename,
because_Cache,
independent_pairFormation,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
unionElimination,
inlFormation,
inrFormation,
applyEquality,
addLevel,
impliesFunctionality,
orFunctionality
Latex:
\mforall{}i:\mBbbZ{}. \mforall{}xs:\mBbbZ{} List. (\muparrow{}int-list-member(i;xs) \mLeftarrow{}{}\mRightarrow{} (i \mmember{} xs))
Date html generated:
2018_05_21-PM-07_31_48
Last ObjectModification:
2017_07_26-PM-05_07_00
Theory : general
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