Nuprl Lemma : subtype_partial_sqtype_base
∀T:Type. ((T ⊆r Base) ⇒ (partial(T) ⊆r Base))
Proof
Definitions occuring in Statement :
partial: partial(T),
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,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a
Lemmas referenced :
subtype_rel_partial,
base_wf,
partial-base,
subtype_rel_transitivity,
partial_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
because_Cache,
universeEquality
Latex:
\mforall{}T:Type. ((T \msubseteq{}r Base) {}\mRightarrow{} (partial(T) \msubseteq{}r Base))
Date html generated:
2016_05_14-AM-06_09_39
Last ObjectModification:
2015_12_26-AM-11_52_15
Theory : partial_1
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