Nuprl Lemma : mrec-label-cases1
∀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 :
all: ∀x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
mrec_spec: MutualRectypeSpec,
implies: P ⇒ Q,
outl: outl(x),
isl: isl(x),
not: ¬A,
false: False
Lemmas referenced :
mrec-label-cases,
eager-map-is-map,
list_wf,
atom-value-type,
pi1_wf,
apply-alist_wf,
atom-deq_wf,
assert_elim,
btrue_wf,
bfalse_wf,
btrue_neq_bfalse,
istype-less_than,
length_wf,
mrec-spec_wf,
istype-atom,
mrec_spec_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
sqequalRule,
instantiate,
isectElimination,
productEquality,
cumulativity,
atomEquality,
unionEquality,
universeEquality,
independent_isectElimination,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
Error :productIsType,
Error :universeIsType,
unionElimination,
equalityTransitivity,
equalitySymmetry,
Error :equalityIstype,
independent_functionElimination,
Error :dependent_set_memberEquality_alt,
independent_pairFormation,
applyLambdaEquality,
setElimination,
rename,
voidElimination,
Error :setIsType,
natural_numberEquality
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_01
Last ObjectModification:
2019_02_27-PM-02_07_34
Theory : tuples
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