Nuprl Lemma : wellfounded_wf
∀[A:Type]. ∀[r:A ⟶ A ⟶ ℙ]. (WellFnd{i}(A;x,y.r[x;y]) ∈ ℙ')
Proof
Definitions occuring in Statement :
wellfounded: WellFnd{i}(A;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,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
so_apply: x[s],
guard: {T}
Lemmas referenced :
uall_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :universeIsType,
Error :inhabitedIsType,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[r:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (WellFnd\{i\}(A;x,y.r[x;y]) \mmember{} \mBbbP{}')
Date html generated:
2019_06_20-AM-11_19_11
Last ObjectModification:
2018_09_26-AM-10_41_44
Theory : well_fnd
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