Nuprl Lemma : list_ind_reverse_unfold1
∀[A,B:Type].
∀nilcase:B. ∀F:B ⟶ (A List) ⟶ A ⟶ B. ∀L:A List.
(list_ind_reverse(L;nilcase;F) ~ if (||L|| =z 0)
then nilcase
else F list_ind_reverse(firstn(||L|| - 1;L);nilcase;F) firstn(||L|| - 1;L) last(L)
fi )
Proof
Definitions occuring in Statement :
list_ind_reverse: list_ind_reverse(L;nilcase;R),
firstn: firstn(n;as),
last: last(L),
length: ||as||,
list: T List,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
subtract: n - m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
list_ind_reverse: list_ind_reverse(L;nilcase;R)
Lemmas referenced :
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
functionEquality,
lambdaEquality,
dependent_functionElimination,
sqequalAxiom,
because_Cache,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:Type].
\mforall{}nilcase:B. \mforall{}F:B {}\mrightarrow{} (A List) {}\mrightarrow{} A {}\mrightarrow{} B. \mforall{}L:A List.
(list\_ind\_reverse(L;nilcase;F) \msim{} if (||L|| =\msubz{} 0)
then nilcase
else F list\_ind\_reverse(firstn(||L|| - 1;L);nilcase;F) firstn(||L|| - 1;L) last(L)
fi )
Date html generated:
2016_05_14-PM-02_59_55
Last ObjectModification:
2015_12_26-PM-01_58_35
Theory : list_1
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