Nuprl Lemma : fl-morph-fl0
∀[J,I:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[x:names(I)]. (((x=0))<f> = dM-to-FL(J;¬(f x)) ∈ Point(face_lattice(J)))
Proof
Definitions occuring in Statement :
fl-morph: <f>,
dM-to-FL: dM-to-FL(I;z),
fl0: (x=0),
face_lattice: face_lattice(I),
names-hom: I ⟶ J,
names-deq: NamesDeq,
names: names(I),
dm-neg: ¬(x),
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,
fl0: (x=0)
Lemmas referenced :
fl-morph-face-lattice0,
names_wf,
names-hom_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,
isect_memberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[J,I:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[x:names(I)]. (((x=0))<f> = dM-to-FL(J;\mneg{}(f x)))
Date html generated:
2016_05_18-PM-00_14_30
Last ObjectModification:
2015_12_28-PM-03_00_41
Theory : cubical!type!theory
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