Nuprl Lemma : dl-prop-sem_wf
∀[K:Type]. ∀[R:ℕ ⟶ K ⟶ K ⟶ ℙ]. ∀[P:ℕ ⟶ K ⟶ ℙ]. ∀[phi:Prop]. ([|phi|] ∈ K ⟶ ℙ)
Proof
Definitions occuring in Statement :
dl-prop-sem: [|phi|],
dl-prop: Prop,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dl-prop-sem: [|phi|],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
dl-kind: dl-kind(d),
mobj-kind: mobj-kind(x),
pi1: fst(t),
dl-prop-obj: prop(x),
bfalse: ff,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
dl-sem_wf,
istype-nat,
dl-prop-obj_wf,
dl-prop_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality_alt,
hypothesis,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
functionIsType,
universeEquality,
because_Cache,
instantiate
Latex:
\mforall{}[K:Type]. \mforall{}[R:\mBbbN{} {}\mrightarrow{} K {}\mrightarrow{} K {}\mrightarrow{} \mBbbP{}]. \mforall{}[P:\mBbbN{} {}\mrightarrow{} K {}\mrightarrow{} \mBbbP{}]. \mforall{}[phi:Prop]. ([|phi|] \mmember{} K {}\mrightarrow{} \mBbbP{})
Date html generated:
2019_10_15-AM-11_43_44
Last ObjectModification:
2019_03_26-AM-11_44_34
Theory : dynamic!logic
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