Nuprl Lemma : k-subtype_wf
∀[k:ℕ]. ∀[A,B:ℕk ⟶ Type]. (A ⊆ B ∈ ℙ)
Proof
Definitions occuring in Statement :
k-subtype: A ⊆ B,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
k-subtype: A ⊆ B,
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
int_seg_wf,
subtype_rel_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[A,B:\mBbbN{}k {}\mrightarrow{} Type]. (A \msubseteq{} B \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-00_08_47
Last ObjectModification:
2017_10_18-PM-02_31_15
Theory : co-recursion
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