Nuprl Lemma : confluent-equiv_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (confluent-equiv(T;x,y.R[x;y]) ∈ T ⟶ T ⟶ ℙ)
Proof
Definitions occuring in Statement :
confluent-equiv: confluent-equiv(T;x,y.R[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
confluent-equiv: confluent-equiv(T;x,y.R[x; y]),
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_self,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality_alt,
productEquality,
hypothesisEquality,
applyEquality,
hypothesis,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
inhabitedIsType,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (confluent-equiv(T;x,y.R[x;y]) \mmember{} T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_24_46
Last ObjectModification:
2019_08_16-PM-03_05_46
Theory : relations2
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