Nuprl Lemma : firstn_last_sq
∀[T:Type]. ∀[L:T List]. L ~ firstn(||L|| - 1;L) @ [last(L)] supposing (¬↑null(L)) ∧ (T ⊆r Base)
Proof
Definitions occuring in Statement :
firstn: firstn(n;as),
last: last(L),
length: ||as||,
null: null(as),
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
assert: ↑b,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
subtract: n - m,
natural_number: $n,
base: Base,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
prop: ℙ
Lemmas referenced :
subtype_base_sq,
list_subtype_base,
firstn_last,
and_wf,
not_wf,
assert_wf,
null_wf,
subtype_rel_wf,
base_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
instantiate,
lemma_by_obid,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. L \msim{} firstn(||L|| - 1;L) @ [last(L)] supposing (\mneg{}\muparrow{}null(L)) \mwedge{} (T \msubseteq{}r Base)
Date html generated:
2016_05_14-PM-02_06_00
Last ObjectModification:
2015_12_26-PM-05_08_20
Theory : list_1
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