Nuprl Lemma : seq-comp_wf
∀[T:Type]. ∀[s:sequence(T)]. ∀[B:Type]. ∀[f:T ⟶ B]. (f o s ∈ sequence(B))
Proof
Definitions occuring in Statement :
seq-comp: f o s,
sequence: sequence(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
seq-comp: f o s,
sequence: sequence(T),
nat: ℕ
Lemmas referenced :
int_seg_wf,
sequence_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
spreadEquality,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairEquality,
hypothesisEquality,
functionEquality,
extract_by_obid,
isectElimination,
natural_numberEquality,
setElimination,
rename,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. \mforall{}[B:Type]. \mforall{}[f:T {}\mrightarrow{} B]. (f o s \mmember{} sequence(B))
Date html generated:
2018_07_25-PM-01_28_25
Last ObjectModification:
2018_06_11-PM-04_22_14
Theory : arithmetic
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