Nuprl Lemma : cWO-induction
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[Q:T ⟶ ℙ]. TI(T;x,y.R[x;y];t.Q[t]) supposing cWO(T;x,y.R[x;y])
Proof
Definitions occuring in Statement :
cWO: cWO(T;x,y.R[x; y]),
TI: TI(T;x,y.R[x; y];t.Q[t]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T
Lemmas referenced :
cWO-induction-extract-sqequal,
cWO-induction_1-ext
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
extract_by_obid,
hypothesis,
instantiate
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[Q:T {}\mrightarrow{} \mBbbP{}]. TI(T;x,y.R[x;y];t.Q[t]) supposing cWO(T;x,y.R[x;y])
Date html generated:
2018_05_21-PM-00_04_11
Last ObjectModification:
2018_05_19-AM-07_10_28
Theory : fun_1
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