Nuprl Lemma : list_induction
∀[T:Type]. ∀[P:(T List) ⟶ ℙ]. (P[[]] ⇒ (∀aaaa:T. ∀LLLL:T List. (P[LLLL] ⇒ P[[aaaa / LLLL]])) ⇒ (∀L:T List. P[L]))
Proof
Definitions occuring in Statement :
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind-general-wf,
all_wf,
list_wf,
cons_wf,
nil_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
rename,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
functionEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P:(T List) {}\mrightarrow{} \mBbbP{}].
(P[[]] {}\mRightarrow{} (\mforall{}aaaa:T. \mforall{}LLLL:T List. (P[LLLL] {}\mRightarrow{} P[[aaaa / LLLL]])) {}\mRightarrow{} (\mforall{}L:T List. P[L]))
Date html generated:
2016_05_14-AM-06_27_12
Last ObjectModification:
2015_12_26-PM-00_41_29
Theory : list_0
Home
Index