Nuprl Lemma : subtype_neg_polymorphism_test
((⋂T:Type. (T ⟶ T ⟶ ℙ)) ⊆r (Top ⟶ Top ⟶ ℙ)) ∧ ((Top ⟶ Top ⟶ ℙ) ⊆r (⋂T:Type. (T ⟶ T ⟶ ℙ)))
Proof
Definitions occuring in Statement :
subtype_rel: A ⊆r B,
top: Top,
prop: ℙ,
and: P ∧ Q,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
and: P ∧ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x]
Lemmas referenced :
top_wf,
subtype_rel_dep_function,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaEquality,
isectElimination,
cut,
lemma_by_obid,
hypothesis,
equalityTransitivity,
equalitySymmetry,
isectEquality,
universeEquality,
functionEquality,
cumulativity,
hypothesisEquality,
isect_memberEquality,
applyEquality,
thin,
instantiate,
sqequalHypSubstitution,
sqequalRule,
independent_isectElimination,
voidElimination,
voidEquality,
lambdaFormation,
because_Cache
Latex:
((\mcap{}T:Type. (T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{})) \msubseteq{}r (Top {}\mrightarrow{} Top {}\mrightarrow{} \mBbbP{})) \mwedge{} ((Top {}\mrightarrow{} Top {}\mrightarrow{} \mBbbP{}) \msubseteq{}r (\mcap{}T:Type. (T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{})))
Date html generated:
2016_05_15-PM-07_48_57
Last ObjectModification:
2015_12_27-AM-11_07_34
Theory : general
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