Nuprl Lemma : mrec-label-cases1-ext
∀s:MutualRectypeSpec. ∀n:Atom. ∀lbl:{lbl:Atom| 0 < ||mrec-spec(s;lbl;n)||} .
(lbl ∈ eager-map(λp.(fst(p));outl(apply-alist(AtomDeq;s;n))))
Proof
Definitions occuring in Statement :
mrec-spec: mrec-spec(L;lbl;p),
mrec_spec: MutualRectypeSpec,
apply-alist: apply-alist(eq;L;x),
l_member: (x ∈ l),
length: ||as||,
eager-map: eager-map(f;as),
atom-deq: AtomDeq,
outl: outl(x),
less_than: a < b,
pi1: fst(t),
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
lambda: λx.A[x],
natural_number: $n,
atom: Atom
Definitions unfolded in proof :
member: t ∈ T,
atom-deq: AtomDeq,
apply-alist: apply-alist(eq;L;x),
it: ⋅,
ifthenelse: if b then t else f fi ,
spreadn: spread3,
mrec-member: mrec-member(s;n;lbl),
mrec-label-cases1,
mrec-label-cases,
sq_stable__l_member,
decidable__atom_equal,
sq_stable_from_decidable,
decidable__l_member,
sq_stable__from_stable,
stable__from_decidable,
list_induction,
decidable_functionality,
nil_member,
decidable__false,
cons_member,
decidable__or,
iff_preserves_decidability,
any: any x,
decidable__assert,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
mrec-label-cases1,
lifting-strict-decide,
istype-void,
strict4-decide,
lifting-strict-atom_eq,
mrec-label-cases,
sq_stable__l_member,
decidable__atom_equal,
sq_stable_from_decidable,
decidable__l_member,
sq_stable__from_stable,
stable__from_decidable,
list_induction,
decidable_functionality,
nil_member,
decidable__false,
cons_member,
decidable__or,
iff_preserves_decidability,
decidable__assert
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
Error :isect_memberEquality_alt,
voidElimination,
independent_isectElimination
Latex:
\mforall{}s:MutualRectypeSpec. \mforall{}n:Atom. \mforall{}lbl:\{lbl:Atom| 0 < ||mrec-spec(s;lbl;n)||\} .
(lbl \mmember{} eager-map(\mlambda{}p.(fst(p));outl(apply-alist(AtomDeq;s;n))))
Date html generated:
2019_06_20-PM-02_15_06
Last ObjectModification:
2019_03_26-AM-06_46_02
Theory : tuples
Home
Index