Nuprl Lemma : sorted-seq_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[s:sequence(T)]. (sorted-seq(x,y.R[x;y];s) ∈ ℙ)
Proof
Definitions occuring in Statement :
sorted-seq: sorted-seq(x,y.R[x; y];s),
sequence: sequence(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sorted-seq: sorted-seq(x,y.R[x; y];s),
prop: ℙ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
implies: P ⇒ Q,
int_seg: {i..j-},
so_apply: x[s1;s2]
Lemmas referenced :
int_seg_wf,
seq-len_wf,
less_than_wf,
seq-item_wf,
sequence_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
hypothesis,
applyEquality,
Error :lambdaEquality_alt,
setElimination,
rename,
Error :inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
because_Cache,
axiomEquality,
Error :universeIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :functionIsType,
universeEquality,
instantiate
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[s:sequence(T)]. (sorted-seq(x,y.R[x;y];s) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_26_54
Last ObjectModification:
2019_01_15-AM-11_10_56
Theory : arithmetic
Home
Index