Nuprl Lemma : last-cons
∀[x:Top]. ∀[as:Top List]. (last([x / as]) ~ if null(as) then x else last(as) fi )
Proof
Definitions occuring in Statement :
last: last(L),
null: null(as),
cons: [a / b],
list: T List,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
last: last(L),
all: ∀x:A. B[x],
or: P ∨ Q,
top: Top,
select: L[n],
uimplies: b supposing a,
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
ifthenelse: if b then t else f fi ,
btrue: tt,
subtract: n - m,
cons: [a / b],
bfalse: ff,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
decidable: Dec(P),
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ
Lemmas referenced :
lelt_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermAdd_wf,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
non_neg_length,
cons_wf,
select_cons_tl_sq,
length_wf,
add-subtract-cancel,
list_wf,
null_cons_lemma,
product_subtype_list,
base_wf,
stuck-spread,
null_nil_lemma,
length_of_nil_lemma,
length_of_cons_lemma,
list-cases,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
baseClosed,
independent_isectElimination,
lambdaFormation,
promote_hyp,
hypothesis_subsumption,
productElimination,
sqequalAxiom,
because_Cache,
addEquality,
natural_numberEquality,
dependent_set_memberEquality,
independent_pairFormation,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll
Latex:
\mforall{}[x:Top]. \mforall{}[as:Top List]. (last([x / as]) \msim{} if null(as) then x else last(as) fi )
Date html generated:
2016_05_14-PM-01_36_35
Last ObjectModification:
2016_01_15-AM-08_24_24
Theory : list_1
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