Nuprl Lemma : weakly-decidable-nset_wf
∀[K:Type]. (WD(K) ∈ ℙ)
Proof
Definitions occuring in Statement :
weakly-decidable-nset: WD(K),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
squash: ↓T,
less_than: a < b,
le: A ≤ B,
lelt: i ≤ j < k,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
or: P ∨ Q,
uimplies: b supposing a,
nat: ℕ,
guard: {T},
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
and: P ∧ Q,
prop: ℙ,
weakly-decidable-nset: WD(K),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
not_wf,
int_subtype_base,
istype-int,
lelt_wf,
set_subtype_base,
equal-wf-base,
subtype_rel_transitivity,
istype-nat,
int_seg_wf,
nat_wf,
subtype_rel_wf
Rules used in proof :
universeEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
imageElimination,
productElimination,
unionEquality,
independent_isectElimination,
intEquality,
rename,
setElimination,
Error :lambdaEquality_alt,
applyEquality,
functionEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:Type]. (WD(K) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-03_01_53
Last ObjectModification:
2019_06_13-PM-00_36_48
Theory : continuity
Home
Index