Nuprl Lemma : all-accessible-iff-weak-TI
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (∀t:T. accessible(T;x,y.R[x;y];t) ⇐⇒ ∀[P:T ⟶ ℙ]. weak-TI(T;x,y.R[y;x];t.P[t]))
Proof
Definitions occuring in Statement :
accessible: accessible(T;x,y.R[x; y];t),
weak-TI: weak-TI(T;x,y.R[x; y];t.Q[t]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
weak-TI: weak-TI(T;x,y.R[x; y];t.Q[t])
Lemmas referenced :
all-accessible-iff-induction
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}].
(\mforall{}t:T. accessible(T;x,y.R[x;y];t) \mLeftarrow{}{}\mRightarrow{} \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. weak-TI(T;x,y.R[y;x];t.P[t]))
Date html generated:
2016_05_14-AM-06_18_52
Last ObjectModification:
2015_12_26-PM-00_02_41
Theory : co-recursion
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