Nuprl Lemma : strongwellfounded_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ Type]. (SWellFounded(R[x;y]) ∈ ℙ)
Proof
Definitions occuring in Statement :
strongwellfounded: SWellFounded(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 :
strongwellfounded: SWellFounded(R[x; y]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
exists_wf,
nat_wf,
all_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
universeEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} Type]. (SWellFounded(R[x;y]) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_52_11
Last ObjectModification:
2015_12_26-PM-06_57_19
Theory : relations2
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