Nuprl Lemma : partial-strong-subtype-base
∀[T:Type]. ((T ⊆r Base) ⇒ strong-subtype(partial(T);Base))
Proof
Definitions occuring in Statement :
partial: partial(T),
strong-subtype: strong-subtype(A;B),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
subtype_rel_wf,
base_wf,
strong-subtype_witness,
partial_wf,
subtype_partial_sqtype_base,
exists_wf,
equal-wf-base-T,
subtype_base_sq,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
independent_pairFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
universeEquality,
setEquality,
applyEquality,
setElimination,
rename,
productElimination,
instantiate,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. ((T \msubseteq{}r Base) {}\mRightarrow{} strong-subtype(partial(T);Base))
Date html generated:
2018_05_21-PM-00_05_13
Last ObjectModification:
2017_10_30-AM-00_43_35
Theory : partial_1
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