Nuprl Lemma : isdM1_wf
∀[I:fset(ℕ)]. ∀[x:Point(dM(I))]. (isdM1(x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
isdM1: isdM1(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,
top: Top,
isdM1: isdM1(x),
subtype_rel: A ⊆r B,
deq: EqDecider(T),
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s]
Lemmas referenced :
nat_wf,
DeMorgan-algebra-axioms_wf,
lattice-join_wf,
lattice-meet_wf,
equal_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure_wf,
subtype_rel_transitivity,
DeMorgan-algebra-structure-subtype,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
DeMorgan-algebra-structure_wf,
subtype_rel_set,
dM_wf,
lattice-point_wf,
empty-fset_wf,
fset-singleton_wf,
deq_wf,
names-deq_wf,
union-deq_wf,
names_wf,
fset_wf,
deq-fset_wf,
dM-point
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
applyEquality,
unionEquality,
hypothesisEquality,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
because_Cache
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:Point(dM(I))]. (isdM1(x) \mmember{} \mBbbB{})
Date html generated:
2016_05_18-AM-11_56_56
Last ObjectModification:
2016_02_04-PM-06_16_02
Theory : cubical!type!theory
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