Nuprl Lemma : dM-to-FL-1
∀[I:fset(ℕ)]. (dM-to-FL(I;1) = 1 ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
dM-to-FL: dM-to-FL(I;z),
face_lattice: face_lattice(I),
dM: dM(I),
lattice-1: 1,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uiff: uiff(P;Q),
so_apply: x[s],
uimplies: b supposing a,
guard: {T},
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
DeMorgan-algebra: DeMorganAlgebra,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
dM-to-FL-eq-1,
lattice-1_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
bounded-lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-point_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
fset_wf,
nat_wf
Rules used in proof :
productElimination,
because_Cache,
universeEquality,
cumulativity,
independent_isectElimination,
productEquality,
lambdaEquality,
instantiate,
sqequalRule,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:fset(\mBbbN{})]. (dM-to-FL(I;1) = 1)
Date html generated:
2016_05_18-PM-00_12_48
Last ObjectModification:
2016_04_18-PM-07_08_52
Theory : cubical!type!theory
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