Nuprl Lemma : dl-same-sem_wf
∀[x:dl-Obj()]. ∀[K:Type]. ∀[r,s:if dl-kind(x) =a "prog" then K ⟶ K ⟶ ℙ else K ⟶ ℙ fi ]. (dl-same-sem(x;K;r;s) ∈ ℙ)
Proof
Definitions occuring in Statement :
dl-same-sem: dl-same-sem(x;K;r;s),
dl-kind: dl-kind(d),
dl-Obj: dl-Obj(),
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
uall: ∀[x:A]. B[x],
prop: ℙ,
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-same-sem: dl-same-sem(x;K;r;s),
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
subtype_rel: A ⊆r B
Lemmas referenced :
equal-wf-base,
all_wf,
iff_wf,
subtype_base_sq,
atom_subtype_base,
ifthenelse_wf,
eq_atom_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
hypothesisEquality,
lambdaEquality_alt,
instantiate,
cumulativity,
atomEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
applyEquality,
inhabitedIsType,
universeIsType,
baseClosed,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
setElimination,
rename,
tokenEquality,
universeEquality
Latex:
\mforall{}[x:dl-Obj()]. \mforall{}[K:Type]. \mforall{}[r,s:if dl-kind(x) =a "prog" then K {}\mrightarrow{} K {}\mrightarrow{} \mBbbP{} else K {}\mrightarrow{} \mBbbP{} fi ].
(dl-same-sem(x;K;r;s) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-11_43_38
Last ObjectModification:
2019_03_26-AM-11_28_14
Theory : dynamic!logic
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