Nuprl Lemma : isdM0_wf
∀[I:fset(ℕ)]. ∀[x:Point(dM(I))]. (isdM0(x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
isdM0: isdM0(x),
dM: dM(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
top: Top,
isdM0: isdM0(x),
fset-null: fset-null(s)
Lemmas referenced :
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
fset_wf,
nat_wf,
dM-point,
fset-null_wf,
names_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
because_Cache,
isect_memberEquality,
voidElimination,
voidEquality,
setElimination,
rename,
unionEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:Point(dM(I))]. (isdM0(x) \mmember{} \mBbbB{})
Date html generated:
2016_05_18-AM-11_56_43
Last ObjectModification:
2015_12_28-PM-03_08_45
Theory : cubical!type!theory
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