Nuprl Lemma : accessible-inversion
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[u:T]. ∀v:T. (accessible(T;x,y.R[x;y];u) ⇒ R[v;u] ⇒ accessible(T;x,y.R[x;y];v))
Proof
Definitions occuring in Statement :
accessible: accessible(T;x,y.R[x; y];t),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y]
Lemmas referenced :
accessible-iff,
accessible_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
lambdaFormation,
independent_functionElimination,
dependent_functionElimination,
applyEquality,
sqequalRule,
lambdaEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[u:T].
\mforall{}v:T. (accessible(T;x,y.R[x;y];u) {}\mRightarrow{} R[v;u] {}\mRightarrow{} accessible(T;x,y.R[x;y];v))
Date html generated:
2016_05_14-AM-06_18_44
Last ObjectModification:
2015_12_26-PM-00_02_53
Theory : co-recursion
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