Nuprl Lemma : co-list-islist-induction1
∀[A:Type]. ∀[P:co-list-islist(A) ⟶ ℙ].
(P[conil()] ⇒ (∀L:co-list-islist(A). ∀a:A. (P[L] ⇒ P[cocons(a;L)])) ⇒ (∀L:co-list-islist(A). P[L]))
Proof
Definitions occuring in Statement :
cocons: cocons(a;L),
conil: conil(),
co-list-islist: co-list-islist(T),
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,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
subtype_rel: A ⊆r B,
so_apply: x[s1;s2;s3]
Lemmas referenced :
co-list-islist_wf,
all_wf,
cocons_wf,
conil_wf,
list_ind-wf-co-list-islist2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
functionEquality,
applyEquality,
cumulativity,
universeEquality,
rename,
introduction
Latex:
\mforall{}[A:Type]. \mforall{}[P:co-list-islist(A) {}\mrightarrow{} \mBbbP{}].
(P[conil()]
{}\mRightarrow{} (\mforall{}L:co-list-islist(A). \mforall{}a:A. (P[L] {}\mRightarrow{} P[cocons(a;L)]))
{}\mRightarrow{} (\mforall{}L:co-list-islist(A). P[L]))
Date html generated:
2016_05_15-PM-10_11_11
Last ObjectModification:
2015_12_27-PM-05_58_42
Theory : eval!all
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