Nuprl Lemma : fl-morph-comp-dM-lift
∀[I,J:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[z:Point(dM(I))].
((dM-to-FL(I;z))<f> = dM-to-FL(J;dM-lift(J;I;f) z) ∈ Point(face_lattice(J)))
Proof
Definitions occuring in Statement :
fl-morph: <f>,
dM-to-FL: dM-to-FL(I;z),
face_lattice: face_lattice(I),
dM-lift: dM-lift(I;J;f),
names-hom: I ⟶ J,
dM: dM(I),
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,
so_lambda: λ2x.t[x],
DeMorgan-algebra: DeMorganAlgebra,
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
dma-hom: dma-hom(dma1;dma2),
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
names-hom: I ⟶ J,
all: ∀x:A. B[x],
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
fl-morph-comp-1,
dM-lift_wf,
all_wf,
equal_wf,
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
dM_inc_wf,
squash_wf,
true_wf,
dM-lift-inc,
iff_weakening_equal,
names_wf,
names-hom_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
sqequalRule,
instantiate,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
lambdaFormation,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[z:Point(dM(I))]. ((dM-to-FL(I;z))<f> = dM-to-FL(J;dM-lift(J;I;f) z))
Date html generated:
2017_10_05-AM-01_14_15
Last ObjectModification:
2017_07_28-AM-09_31_27
Theory : cubical!type!theory
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