Nuprl Lemma : last_cons
∀[T:Type]. ∀[L:T List]. ∀[x:T]. last([x / L]) = last(L) ∈ T supposing ¬↑null(L)
Proof
Definitions occuring in Statement :
last: last(L),
null: null(as),
cons: [a / b],
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
prop: ℙ,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
last_cons2,
subtype_rel_list,
top_wf,
null_wf,
bool_wf,
eqtt_to_assert,
assert_of_null,
null_nil_lemma,
btrue_wf,
not_assert_elim,
and_wf,
equal_wf,
list_wf,
btrue_neq_bfalse,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
equal-wf-T-base,
last_wf,
assert_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
cumulativity,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
setElimination,
rename,
independent_functionElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
baseClosed,
addLevel,
impliesFunctionality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[x:T]. last([x / L]) = last(L) supposing \mneg{}\muparrow{}null(L)
Date html generated:
2017_04_14-AM-08_39_56
Last ObjectModification:
2017_02_27-PM-03_30_04
Theory : list_0
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