Nuprl Lemma : decidable__equal_face_lattice
∀[I:fset(ℕ)]. ∀x,y:Point(face_lattice(I)). Dec(x = y ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
face_lattice: face_lattice(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
deq-implies,
lattice-point_wf,
face_lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
fset_wf,
nat_wf,
face_lattice-deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}x,y:Point(face\_lattice(I)). Dec(x = y)
Date html generated:
2017_02_21-AM-10_32_06
Last ObjectModification:
2017_02_02-PM-01_23_02
Theory : cubical!type!theory
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