Nuprl Lemma : per-partial-subtype
∀A,B:Type. ∀a,b:Base. ((A ⊆r B) ⇒ per-partial(A;a;b) ⇒ per-partial(B;a;b))
Proof
Definitions occuring in Statement :
per-partial: per-partial(T;x;y),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
per-partial: per-partial(T;x;y),
and: P ∧ Q,
uiff: uiff(P;Q),
cand: A c∧ B,
uimplies: b supposing a,
member: t ∈ T,
has-value: (a)↓,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T}
Lemmas referenced :
has-value_wf_base,
equal_functionality_wrt_subtype_rel2,
per-partial_wf,
subtype_rel_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
independent_pairFormation,
isect_memberFormation,
introduction,
independent_isectElimination,
hypothesis,
sqequalRule,
axiomSqleEquality,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
because_Cache,
universeEquality
Latex:
\mforall{}A,B:Type. \mforall{}a,b:Base. ((A \msubseteq{}r B) {}\mRightarrow{} per-partial(A;a;b) {}\mRightarrow{} per-partial(B;a;b))
Date html generated:
2016_05_14-AM-06_09_23
Last ObjectModification:
2015_12_26-AM-11_52_26
Theory : partial_1
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