Nuprl Lemma : canonicalizable-base
∀[T:Type]. ((T ⊆r Base) ⇒ canonicalizable(T))
Proof
Definitions occuring in Statement :
canonicalizable: canonicalizable(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
canonicalizable-iff,
subtype_rel_wf,
base_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_functionElimination,
dependent_pairFormation_alt,
applyEquality,
hypothesis,
sqequalRule,
equalityIstype,
because_Cache,
sqequalBase,
equalitySymmetry,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. ((T \msubseteq{}r Base) {}\mRightarrow{} canonicalizable(T))
Date html generated:
2019_10_15-AM-10_20_02
Last ObjectModification:
2019_08_29-AM-10_57_46
Theory : call!by!value_2
Home
Index