Nuprl Lemma : name-morph-satisfies_wf
∀[I,J:fset(ℕ)]. ∀[psi:Point(face_lattice(I))]. ∀[f:J ⟶ I]. ((psi f) = 1 ∈ ℙ)
Proof
Definitions occuring in Statement :
name-morph-satisfies: (psi f) = 1,
face_lattice: face_lattice(I),
names-hom: I ⟶ J,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph-satisfies: (psi f) = 1,
subtype_rel: A ⊆r B,
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
equal_wf,
lattice-point_wf,
face_lattice_wf,
fl-morph_wf,
bounded-lattice-hom_wf,
bdd-distributive-lattice_wf,
lattice-1_wf,
names-hom_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-meet_wf,
lattice-join_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
lambdaEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
instantiate,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[psi:Point(face\_lattice(I))]. \mforall{}[f:J {}\mrightarrow{} I]. ((psi f) = 1 \mmember{} \mBbbP{})
Date html generated:
2016_05_18-PM-00_19_55
Last ObjectModification:
2015_12_28-PM-02_59_43
Theory : cubical!type!theory
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