Nuprl Lemma : id-is-lattice-hom
∀[l:LatticeStructure]. (λx.x ∈ Hom(l;l))
Proof
Definitions occuring in Statement :
lattice-hom: Hom(l1;l2),
lattice-structure: LatticeStructure,
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-hom: Hom(l1;l2),
and: P ∧ Q,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
lattice-point_wf,
lattice-meet_wf,
lattice-join_wf,
uall_wf,
and_wf,
equal_wf,
lattice-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
lambdaEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
independent_pairFormation,
productElimination,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
applyEquality
Latex:
\mforall{}[l:LatticeStructure]. (\mlambda{}x.x \mmember{} Hom(l;l))
Date html generated:
2020_05_20-AM-08_23_50
Last ObjectModification:
2015_12_28-PM-02_03_38
Theory : lattices
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