Nuprl Lemma : uimplies_subtype
∀[A,B:Type]. ∀[P:ℙ]. (A supposing P ⊆r B) supposing ((A ⊆r B) and P)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
isect_subtype_rel_trivial,
subtype_rel_transitivity,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
independent_isectElimination,
independent_pairFormation,
hypothesis,
isectEquality,
because_Cache,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[P:\mBbbP{}]. (A supposing P \msubseteq{}r B) supposing ((A \msubseteq{}r B) and P)
Date html generated:
2016_05_13-PM-04_10_37
Last ObjectModification:
2015_12_26-AM-11_22_00
Theory : subtype_1
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