Nuprl Lemma : fl-morph-comp2
∀[I,J,K:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[g:K ⟶ J]. ∀[x:Point(face_lattice(I))].
(((x)<f>)<g> = (x)<f ⋅ g> ∈ Point(face_lattice(K)))
Proof
Definitions occuring in Statement :
fl-morph: <f>,
face_lattice: face_lattice(I),
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
compose: f o g,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
fl-morph-comp,
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,
names-hom_wf,
fset_wf,
nat_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
lambdaEquality,
functionEquality,
because_Cache,
sqequalRule,
equalitySymmetry,
instantiate,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[I,J,K:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[g:K {}\mrightarrow{} J]. \mforall{}[x:Point(face\_lattice(I))]. (((x)<f>)<g> = (x)<f \mcdot{} g>)
Date html generated:
2016_05_18-PM-00_15_49
Last ObjectModification:
2015_12_28-PM-03_00_28
Theory : cubical!type!theory
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