Nuprl Lemma : tcWO-induction
∀[T:Type]. ∀[>:T ⟶ T ⟶ ℙ]. ∀[Q:T ⟶ ℙ]. TI(T;x,y.>[x;y];t.Q[t]) supposing tcWO(T;x,y.>[x;y])
Proof
Definitions occuring in Statement :
tcWO: tcWO(T;x,y.>[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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
tcWO: tcWO(T;x,y.>[x; y]),
and: P ∧ Q,
almost-full: AFx,y:T.R[x; y],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
AF-induction2,
tcWO_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
productElimination,
sqequalRule,
lambdaEquality,
applyEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[>:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[Q:T {}\mrightarrow{} \mBbbP{}]. TI(T;x,y.>[x;y];t.Q[t]) supposing tcWO(T;x,y.>[x;y])
Date html generated:
2016_05_13-PM-03_53_02
Last ObjectModification:
2015_12_26-AM-10_16_55
Theory : bar-induction
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