Nuprl Lemma : dl-implies-1_wf
∀[x:Prop]. dl-implies-1(x) ∈ Prop supposing ↑dl-implies?(x)
Proof
Definitions occuring in Statement :
dl-implies-1: dl-implies-1(x),
dl-implies?: dl-implies?(x),
dl-prop: Prop,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
dl-prop: Prop,
mrec: mrec(L;i),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
eager-map: eager-map(f;as),
list_ind: list_ind,
outl: outl(x),
apply-alist: apply-alist(eq;L;x),
dl-Spec: dl-Spec(),
cons: [a / b],
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
pi1: fst(t),
bfalse: ff,
btrue: tt,
pi2: snd(t),
nil: [],
it: ⋅,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
mrec-spec: mrec-spec(L;lbl;p),
top: Top,
mk-prec: mk-prec(lbl;x),
dl-aprop: atm(x),
assert: ↑b,
dl-implies?: dl-implies?(x),
dl-label: dl-label(d),
mobj-label: mobj-label(x),
prec-label: prec-label(x),
mobj-data: mobj-data(x),
dl-prop-obj: prop(x),
false: False,
unit: Unit,
dl-false: 0,
dl-implies: x1 ⇒ x,
true: True,
dl-implies-1: dl-implies-1(x),
select-tuple: x.n,
eq_int: (i =z j),
dl-and: x1 ∧ x,
dl-or: x1 ∨ x,
dl-prog: Prog,
dl-box: [x1] x,
dl-diamond: <x1> x
Lemmas referenced :
prec-ext,
mrec-spec_wf,
dl-Spec_wf,
istype-atom,
mrec-label-cases1-ext,
cons_member,
cons_wf,
nil_wf,
subtype_base_sq,
atom_subtype_base,
atomdeq_reduce_lemma,
istype-void,
map_cons_lemma,
map_nil_lemma,
tupletype_cons_lemma,
null_nil_lemma,
tupletype_nil_lemma,
null_cons_lemma,
member_singleton,
istype-assert,
dl-implies?_wf,
dl-prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
introduction,
extract_by_obid,
isectElimination,
thin,
atomEquality,
sqequalRule,
lambdaEquality_alt,
hypothesis,
hypothesisEquality,
inhabitedIsType,
tokenEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
applyEquality,
dependent_functionElimination,
setElimination,
rename,
independent_functionElimination,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
voidElimination,
equalityElimination,
universeIsType
Latex:
\mforall{}[x:Prop]. dl-implies-1(x) \mmember{} Prop supposing \muparrow{}dl-implies?(x)
Date html generated:
2019_10_15-AM-11_41_12
Last ObjectModification:
2019_03_26-AM-11_24_54
Theory : dynamic!logic
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