Nuprl Lemma : dl-obj-prop_wf
∀[x:dl-Obj()]. dl-obj-prop(x) ∈ Prop supposing dl-kind(x) = "prop" ∈ Atom
Proof
Definitions occuring in Statement :
dl-obj-prop: dl-obj-prop(x),
dl-kind: dl-kind(d),
dl-prop: Prop,
dl-Obj: dl-Obj(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
token: "$token",
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
dl-Obj: dl-Obj(),
mobj: mobj(L),
dl-kind: dl-kind(d),
mobj-kind: mobj-kind(x),
pi1: fst(t),
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
dl-obj-prop: dl-obj-prop(x),
pi2: snd(t),
mtype: mtype(L;i),
apply_alist: apply_alist(eq;L;x),
eager-map: eager-map(f;as),
list_ind: list_ind,
dl-Spec: dl-Spec(),
cons: [a / b],
nil: [],
it: ⋅,
atom-deq: AtomDeq,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
mrec: mrec(L;i),
prec: prec(lbl,p.a[lbl; p];i),
dl-prop: Prop,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
subtype_base_sq,
atom_subtype_base,
dl-prop_wf,
istype-atom,
dl-kind_wf,
set_subtype_base,
l_member_wf,
cons_wf,
nil_wf,
dl-Obj_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
instantiate,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
atomEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
hypothesisEquality,
applyEquality,
lambdaEquality_alt,
hyp_replacement,
universeIsType,
equalityIstype,
tokenEquality,
baseClosed,
sqequalBase
Latex:
\mforall{}[x:dl-Obj()]. dl-obj-prop(x) \mmember{} Prop supposing dl-kind(x) = "prop"
Date html generated:
2019_10_15-AM-11_42_38
Last ObjectModification:
2019_04_04-PM-06_18_17
Theory : dynamic!logic
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