Nuprl Lemma : subtype_rel_not
∀[P,Q:ℙ]. (¬P) ⊆r (¬Q) supposing Q ⇒ (↓P)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
false: False,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T},
squash: ↓T
Lemmas referenced :
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
functionEquality,
sqequalHypSubstitution,
sqequalRule,
hypothesisEquality,
voidEquality,
axiomEquality,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
functionExtensionality,
independent_functionElimination,
imageElimination,
voidElimination
Latex:
\mforall{}[P,Q:\mBbbP{}]. (\mneg{}P) \msubseteq{}r (\mneg{}Q) supposing Q {}\mRightarrow{} (\mdownarrow{}P)
Date html generated:
2016_05_13-PM-03_18_57
Last ObjectModification:
2015_12_26-AM-09_08_05
Theory : subtype_0
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