Nuprl Lemma : is-above_wf
∀[T:Type]. ∀[a:T]. ∀[z:Base]. (is-above(T;a;z) ∈ ℙ)
Proof
Definitions occuring in Statement :
is-above: is-above(T;a;z),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-above: is-above(T;a;z),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
exists_wf,
base_wf,
equal-wf-base-T,
sqle_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
Error :lambdaEquality_alt,
productEquality,
because_Cache,
hypothesisEquality,
Error :inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
Error :isect_memberEquality_alt,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[z:Base]. (is-above(T;a;z) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_28_11
Last ObjectModification:
2018_09_29-PM-11_15_19
Theory : subtype_1
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