Nuprl Lemma : dM-point-subtype
∀[I,J:fset(ℕ)]. Point(dM(I)) ⊆r Point(dM(J)) supposing I ⊆ J
Proof
Definitions occuring in Statement :
dM: dM(I),
lattice-point: Point(l),
f-subset: xs ⊆ ys,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
member: t ∈ T,
top: Top,
union-deq: union-deq(A;B;a;b),
sumdeq: sumdeq(a;b),
prop: ℙ,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
and: P ∧ Q,
guard: {T},
so_apply: x[s],
nat: ℕ
Lemmas referenced :
dM-point,
fset-subtype,
fset_wf,
names_wf,
subtype_rel_union,
names-subtype,
assert_wf,
fset-antichain_wf,
union-deq_wf,
names-deq_wf,
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,
f-subset_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaEquality,
sqequalHypSubstitution,
cut,
lemma_by_obid,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalRule,
setElimination,
rename,
dependent_set_memberEquality,
hypothesisEquality,
applyEquality,
unionEquality,
independent_isectElimination,
because_Cache,
instantiate,
productEquality,
cumulativity,
universeEquality,
intEquality,
natural_numberEquality
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. Point(dM(I)) \msubseteq{}r Point(dM(J)) supposing I \msubseteq{} J
Date html generated:
2016_05_18-AM-11_56_25
Last ObjectModification:
2015_12_28-PM-03_09_10
Theory : cubical!type!theory
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