Nuprl Lemma : subtype_rel_per-class
∀[A,B:Type]. ∀[a:A]. (per-class(A;a) ⊆r per-class(B;a)) supposing A ⊆r B
Proof
Definitions occuring in Statement :
per-class: per-class(T;a),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
per-class: per-class(T;a),
guard: {T},
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
equal_functionality_wrt_subtype_rel2,
equal-wf-base-T,
per-class_wf,
subtype_rel_b-union-right,
base_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesisEquality,
hypothesis,
lemma_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
independent_functionElimination,
applyEquality,
sqequalRule,
cumulativity,
because_Cache,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[a:A]. (per-class(A;a) \msubseteq{}r per-class(B;a)) supposing A \msubseteq{}r B
Date html generated:
2016_05_13-PM-04_12_36
Last ObjectModification:
2015_12_26-AM-11_12_11
Theory : subtype_1
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