Nuprl Lemma : unique-minimal_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[m:T]. (unique-minimal(T;x,y.R[x;y];m) ∈ ℙ)
Proof
Definitions occuring in Statement :
unique-minimal: unique-minimal(T;x,y.R[x; y];m),
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,
unique-minimal: unique-minimal(T;x,y.R[x; y];m),
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
and_wf,
all_wf,
not_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[m:T]. (unique-minimal(T;x,y.R[x;y];m) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-07_50_29
Last ObjectModification:
2015_12_27-AM-11_05_27
Theory : general
Home
Index