Nuprl Lemma : length-lastn
∀[A:Type]. ∀[L:A List]. ∀[n:ℕ]. ||lastn(n;L)|| = n ∈ ℤ supposing n ≤ ||L||
Proof
Definitions occuring in Statement :
lastn: lastn(n;L),
length: ||as||,
list: T List,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
lastn: lastn(n;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
nat: ℕ,
squash: ↓T,
int_iseg: {i...j},
and: P ∧ Q,
cand: A c∧ B,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
le_wf,
length_wf,
nat_wf,
list_wf,
equal_wf,
squash_wf,
true_wf,
length_nth_tl,
subtract_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
iff_weakening_equal,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
cumulativity,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
applyEquality,
lambdaEquality,
imageElimination,
intEquality,
dependent_set_memberEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
productEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}[L:A List]. \mforall{}[n:\mBbbN{}]. ||lastn(n;L)|| = n supposing n \mleq{} ||L||
Date html generated:
2018_05_21-PM-06_31_44
Last ObjectModification:
2017_07_26-PM-04_51_15
Theory : general
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