Nuprl Lemma : dl-sem_wf
∀[K:Type]. ∀[R:ℕ ⟶ K ⟶ K ⟶ ℙ]. ∀[P:ℕ ⟶ K ⟶ ℙ].
(dl-sem(K;n.R[n];m.P[m]) ∈ d:dl-Obj() ⟶ if dl-kind(d) =a "prog" then K ⟶ K ⟶ ℙ else K ⟶ ℙ fi )
Proof
Definitions occuring in Statement :
dl-sem: dl-sem(K;n.R[n];m.P[m]),
dl-kind: dl-kind(d),
dl-Obj: dl-Obj(),
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
token: "$token",
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dl-sem: dl-sem(K;n.R[n];m.P[m]),
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
exists: ∃x:A. B[x],
and: P ∧ Q,
so_apply: x[s1;s2;s3;s4],
or: P ∨ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
dl-ind_wf_definition,
subtype-TYPE,
istype-nat,
subtype_rel_self,
dl-prog_wf,
rel_star_wf,
equal_wf,
dl-prop_wf,
false_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
hypothesis,
applyEquality,
instantiate,
because_Cache,
lambdaEquality_alt,
productEquality,
inhabitedIsType,
universeIsType,
functionIsType,
unionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[K:Type]. \mforall{}[R:\mBbbN{} {}\mrightarrow{} K {}\mrightarrow{} K {}\mrightarrow{} \mBbbP{}]. \mforall{}[P:\mBbbN{} {}\mrightarrow{} K {}\mrightarrow{} \mBbbP{}].
(dl-sem(K;n.R[n];m.P[m]) \mmember{} d:dl-Obj() {}\mrightarrow{} if dl-kind(d) =a "prog" then K {}\mrightarrow{} K {}\mrightarrow{} \mBbbP{} else K {}\mrightarrow{} \mBbbP{} fi )
Date html generated:
2019_10_15-AM-11_43_33
Last ObjectModification:
2019_03_26-AM-11_31_49
Theory : dynamic!logic
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