Nuprl Lemma : dMpair_wf
∀[I:fset(ℕ)]. ∀[i,j:ℕ]. (dMpair(i;j) ∈ Point(dM(I))) supposing (j ∈ I and i ∈ I)
Proof
Definitions occuring in Statement :
dMpair: dMpair(i;j),
dM: dM(I),
lattice-point: Point(l),
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
dMpair-eq-meet,
fset-member_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
fset_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
axiomEquality,
applyEquality,
because_Cache,
isect_memberEquality,
intEquality,
lambdaEquality,
natural_numberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i,j:\mBbbN{}]. (dMpair(i;j) \mmember{} Point(dM(I))) supposing (j \mmember{} I and i \mmember{} I)
Date html generated:
2016_05_18-AM-11_57_18
Last ObjectModification:
2015_12_28-PM-03_08_17
Theory : cubical!type!theory
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