Nuprl Lemma : absolutelyfree-subtype
∀[T:Type]. T ⊆r (ℕ ⟶ ℕ) supposing absolutelyfree{i:l}(T)
Proof
Definitions occuring in Statement :
absolutelyfree: absolutelyfree{i:l}(T),
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
absolutelyfree: absolutelyfree{i:l}(T),
and: P ∧ Q
Lemmas referenced :
absolutelyfree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination
Latex:
\mforall{}[T:Type]. T \msubseteq{}r (\mBbbN{} {}\mrightarrow{} \mBbbN{}) supposing absolutelyfree\{i:l\}(T)
Date html generated:
2017_09_29-PM-06_10_41
Last ObjectModification:
2017_04_21-PM-00_38_04
Theory : continuity
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