Nuprl Lemma : fl-join_wf
∀[I:fset(ℕ)]. ∀[x,y:𝔽(I)]. (fl-join(I;x;y) ∈ 𝔽(I))
Proof
Definitions occuring in Statement :
fl-join: fl-join(I;x;y),
face-presheaf: 𝔽,
I_cube: A(I),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-presheaf: 𝔽,
I_cube: A(I),
functor-ob: functor-ob(F),
pi1: fst(t),
fl-join: fl-join(I;x;y),
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
Lemmas referenced :
I_cube_wf,
face-presheaf_wf,
fset_wf,
nat_wf,
lattice-join_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,
lattice-point_wf,
equal_wf,
lattice-meet_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x,y:\mBbbF{}(I)]. (fl-join(I;x;y) \mmember{} \mBbbF{}(I))
Date html generated:
2016_05_18-PM-00_16_35
Last ObjectModification:
2015_12_28-PM-03_00_11
Theory : cubical!type!theory
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