Nuprl Lemma : mkterm_wf
∀[Op:Type]. ∀[opr:Op]. ∀[bts:(varname() List × term(Op)) List]. (mkterm(opr;bts) ∈ term(Op))
Proof
Definitions occuring in Statement :
mkterm: mkterm(opr;bts),
term: term(opr),
varname: varname(),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mkterm: mkterm(opr;bts),
coterm-fun: coterm-fun(opr;T),
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
term-ext,
varname_wf,
nullvar_wf,
istype-void,
ext-eq_inversion,
term_wf,
coterm-fun_wf,
subtype_rel_weakening,
list_wf,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
inrEquality_alt,
independent_pairEquality,
setIsType,
universeIsType,
sqequalRule,
functionIsType,
equalityIstype,
inhabitedIsType,
applyEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[Op:Type]. \mforall{}[opr:Op]. \mforall{}[bts:(varname() List \mtimes{} term(Op)) List]. (mkterm(opr;bts) \mmember{} term(Op))
Date html generated:
2020_05_19-PM-09_53_41
Last ObjectModification:
2020_03_09-PM-04_08_18
Theory : terms
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