Nuprl Lemma : name-morph-satisfies-join
∀I,J:fset(ℕ). ∀a,b:Point(face_lattice(I)). ∀f:J ⟶ I. ((fl-join(I;a;b) f) = 1 ⇐⇒ (a f) = 1 ∨ (b f) = 1)
Proof
Definitions occuring in Statement :
name-morph-satisfies: (psi f) = 1,
fl-join: fl-join(I;x;y),
face_lattice: face_lattice(I),
names-hom: I ⟶ J,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
name-morph-satisfies: (psi f) = 1,
fl-join: fl-join(I;x;y),
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
true: True,
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
squash: ↓T,
guard: {T}
Lemmas referenced :
names-hom_wf,
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,
fset_wf,
nat_wf,
lattice-1_wf,
bdd-distributive-lattice_wf,
or_wf,
fl-morph_wf,
bounded-lattice-hom_wf,
face_lattice-1-join-irreducible,
iff_wf,
squash_wf,
true_wf,
fl-morph-join,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
natural_numberEquality,
independent_pairFormation,
addLevel,
productElimination,
impliesFunctionality,
dependent_functionElimination,
independent_functionElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed
Latex:
\mforall{}I,J:fset(\mBbbN{}). \mforall{}a,b:Point(face\_lattice(I)). \mforall{}f:J {}\mrightarrow{} I.
((fl-join(I;a;b) f) = 1 \mLeftarrow{}{}\mRightarrow{} (a f) = 1 \mvee{} (b f) = 1)
Date html generated:
2017_10_05-AM-01_17_39
Last ObjectModification:
2017_07_28-AM-09_33_14
Theory : cubical!type!theory
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