Nuprl Lemma : dM-lift_wf2
∀[I,J:fset(ℕ)]. ∀[f:I ⟶ J]. (dM-lift(I;J;f) ∈ Point(dM(J)) ⟶ Point(dM(I)))
Proof
Definitions occuring in Statement :
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],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
dma-hom: dma-hom(dma1;dma2),
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
DeMorgan-algebra: DeMorganAlgebra,
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
names-hom: I ⟶ J
Lemmas referenced :
dM-lift_wf,
dma-hom_wf,
dM_wf,
all_wf,
names_wf,
equal_wf,
lattice-point_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,
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,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
dependent_functionElimination,
sqequalRule,
instantiate,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:I {}\mrightarrow{} J]. (dM-lift(I;J;f) \mmember{} Point(dM(J)) {}\mrightarrow{} Point(dM(I)))
Date html generated:
2018_05_23-AM-08_27_39
Last ObjectModification:
2018_05_20-PM-05_35_42
Theory : cubical!type!theory
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