Nuprl Lemma : strong-subtype-partial
∀[T:Type]. (value-type(T) ⇒ strong-subtype(T;partial(T)))
Proof
Definitions occuring in Statement :
partial: partial(T),
strong-subtype: strong-subtype(A;B),
value-type: value-type(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
inclusion-partial,
partial_wf,
exists_wf,
equal_wf,
value-type_wf,
strong-subtype_witness,
termination,
value-type-has-value,
has-value_wf-partial
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
independent_pairFormation,
lambdaEquality,
setEquality,
cumulativity,
sqequalRule,
applyEquality,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
universeEquality,
setElimination,
rename,
productElimination,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality
Latex:
\mforall{}[T:Type]. (value-type(T) {}\mRightarrow{} strong-subtype(T;partial(T)))
Date html generated:
2016_10_21-AM-09_44_52
Last ObjectModification:
2016_07_12-AM-05_04_43
Theory : partial_1
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