Nuprl Lemma : implies-nh-comp-satisfies
∀[I,J,K:fset(ℕ)]. ∀[psi:Point(face_lattice(I))]. ∀[f:J ⟶ I]. ∀[g:K ⟶ J]. (psi f ⋅ g) = 1 supposing (psi f) = 1
Proof
Definitions occuring in Statement :
name-morph-satisfies: (psi f) = 1,
face_lattice: face_lattice(I),
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
name-morph-satisfies: (psi f) = 1,
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
compose: f o g,
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2)
Lemmas referenced :
name-morph-satisfies_wf,
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,
squash_wf,
true_wf,
fl-morph-comp,
lattice-1_wf,
bdd-distributive-lattice_wf,
iff_weakening_equal,
fl-morph_wf,
bounded-lattice-hom_wf,
fl-morph-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
axiomEquality,
hypothesis,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination,
imageElimination,
setElimination,
rename,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[I,J,K:fset(\mBbbN{})]. \mforall{}[psi:Point(face\_lattice(I))]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[g:K {}\mrightarrow{} J].
(psi f \mcdot{} g) = 1 supposing (psi f) = 1
Date html generated:
2017_10_05-AM-01_17_32
Last ObjectModification:
2017_07_28-AM-09_33_10
Theory : cubical!type!theory
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