Nuprl Lemma : prec-sq
∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)]. ∀[i:P]. ∀[x:prec(lbl,p.a[lbl;p];i)].
(x ~ mk-prec(prec-label(x);prec-tuple(x)))
Proof
Definitions occuring in Statement :
prec-tuple: prec-tuple(x),
prec-label: prec-label(x),
mk-prec: mk-prec(lbl;x),
prec: prec(lbl,p.a[lbl; p];i),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
function: x:A ⟶ B[x],
union: left + right,
atom: Atom,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
guard: {T},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
prec-tuple: prec-tuple(x),
prec-label: prec-label(x),
mk-prec: mk-prec(lbl;x),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
prec-ext,
subtype_rel_weakening,
prec_wf,
istype-atom,
less_than_wf,
length_wf,
tuple-type_wf,
map_wf,
list_wf,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
productEquality,
setEquality,
atomEquality,
natural_numberEquality,
instantiate,
unionEquality,
cumulativity,
universeEquality,
equalityTransitivity,
equalitySymmetry,
Error :lambdaFormation_alt,
unionElimination,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
Error :unionIsType,
setElimination,
rename,
independent_isectElimination,
productElimination,
axiomSqEquality,
Error :universeIsType,
Error :functionIsType
Latex:
\mforall{}[P:Type]. \mforall{}[a:Atom {}\mrightarrow{} P {}\mrightarrow{} ((P + P + Type) List)]. \mforall{}[i:P]. \mforall{}[x:prec(lbl,p.a[lbl;p];i)].
(x \msim{} mk-prec(prec-label(x);prec-tuple(x)))
Date html generated:
2019_06_20-PM-02_05_33
Last ObjectModification:
2019_02_28-PM-03_20_53
Theory : tuples
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