Nuprl Lemma : uwellfounded_wf
∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ]. (uWellFnd(A;x,y.R[x;y]) ∈ ℙ')
Proof
Definitions occuring in Statement :
uwellfounded: uWellFnd(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,
uwellfounded: uWellFnd(A;x,y.R[x; y]),
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
uall_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaEquality,
setEquality,
applyEquality,
hypothesis,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (uWellFnd(A;x,y.R[x;y]) \mmember{} \mBbbP{}')
Date html generated:
2016_05_13-PM-03_18_12
Last ObjectModification:
2015_12_26-AM-09_06_50
Theory : well_fnd
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