Nuprl Lemma : t-sqle_wf
∀[T:Type]. ∀[a,b:T]. (t-sqle(T;a;b) ∈ ℙ)
Proof
Definitions occuring in Statement :
t-sqle: t-sqle(T;a;b),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
t-sqle: t-sqle(T;a;b),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
per-class: per-class(T;a),
so_apply: x[s]
Lemmas referenced :
squash_wf,
exists_wf,
per-class_wf,
subtype_rel_b-union-right,
base_wf,
sqle_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
lambdaEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a,b:T]. (t-sqle(T;a;b) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-04_12_46
Last ObjectModification:
2015_12_26-AM-11_11_55
Theory : subtype_1
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