Nuprl Lemma : name-morph-satisfies-fl0
∀[I,J:fset(ℕ)]. ∀[i:names(I)]. ∀[f:J ⟶ I]. uiff(((i=0) f) = 1;(f i) = 0 ∈ Point(dM(J)))
Proof
Definitions occuring in Statement :
name-morph-satisfies: (psi f) = 1,
fl0: (x=0),
names-hom: I ⟶ J,
dM0: 0,
dM: dM(I),
names: names(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
name-morph-satisfies: (psi f) = 1,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
names-hom: I ⟶ J,
uiff: uiff(P;Q)
Lemmas referenced :
nat_wf,
fset_wf,
names_wf,
names-hom_wf,
dM0_wf,
DeMorgan-algebra-axioms_wf,
lattice-join_wf,
lattice-meet_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure_wf,
subtype_rel_transitivity,
DeMorgan-algebra-structure-subtype,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
DeMorgan-algebra-structure_wf,
subtype_rel_set,
dM_wf,
lattice-point_wf,
equal_wf,
fl0_wf,
name-morph-satisfies_wf,
fl-morph-fl0-is-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
because_Cache,
isect_memberFormation,
introduction,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[i:names(I)]. \mforall{}[f:J {}\mrightarrow{} I]. uiff(((i=0) f) = 1;(f i) = 0)
Date html generated:
2016_05_18-PM-00_20_19
Last ObjectModification:
2016_01_26-PM-03_12_09
Theory : cubical!type!theory
Home
Index