Nuprl Lemma : term-opr_wf
∀[opr:Type]. ∀[t:term(opr)]. term-opr(t) ∈ opr supposing ¬↑isvarterm(t)
Proof
Definitions occuring in Statement :
term-opr: term-opr(t),
isvarterm: isvarterm(t),
term: term(opr),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
coterm-fun: coterm-fun(opr;T),
isvarterm: isvarterm(t),
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
not: ¬A,
implies: P ⇒ Q,
true: True,
false: False,
bfalse: ff,
term-opr: term-opr(t),
outr: outr(x),
pi1: fst(t)
Lemmas referenced :
term-ext,
ext-eq_inversion,
term_wf,
coterm-fun_wf,
subtype_rel_weakening,
istype-assert,
isvarterm_wf,
istype-void,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
promote_hyp,
hypothesis_subsumption,
hypothesis,
independent_isectElimination,
applyEquality,
because_Cache,
sqequalRule,
unionElimination,
independent_functionElimination,
natural_numberEquality,
voidElimination,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[t:term(opr)]. term-opr(t) \mmember{} opr supposing \mneg{}\muparrow{}isvarterm(t)
Date html generated:
2020_05_19-PM-09_53_54
Last ObjectModification:
2020_03_09-PM-04_08_24
Theory : terms
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