Nuprl Lemma : per-class-base
∀[T:Type]. ∀[a:T]. ∀[b:per-class(T;a)]. (b ~ a) supposing T ⊆r Base
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],
base: Base,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
per-class: per-class(T;a),
guard: {T},
implies: P ⇒ Q,
sq_type: SQType(T),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_base_sq,
subtype_rel_self,
equal_functionality_wrt_subtype_rel2,
base_wf,
per-class_wf,
subtype_rel_b-union-left,
subtype_rel_transitivity,
b-union_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
instantiate,
lemma_by_obid,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
dependent_functionElimination,
sqequalAxiom,
applyEquality,
sqequalRule,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[b:per-class(T;a)]. (b \msim{} a) supposing T \msubseteq{}r Base
Date html generated:
2016_05_13-PM-04_12_42
Last ObjectModification:
2015_12_26-AM-11_11_51
Theory : subtype_1
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