Nuprl Lemma : shift-seq_wf
∀[c:(ℕ ⟶ ℕ) ⟶ ℕ]. ∀[a:ℕ ⟶ ℕ]. (shift-seq(c;a) ∈ ℕ ⟶ ℕ)
Proof
Definitions occuring in Statement :
shift-seq: shift-seq(c;a),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
shift-seq: shift-seq(c;a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
cons-nat-seq_wf,
nat_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
functionEquality,
hypothesisEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[c:(\mBbbN{} {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} \mBbbN{}]. \mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (shift-seq(c;a) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbN{})
Date html generated:
2017_04_20-AM-07_35_35
Last ObjectModification:
2017_04_07-PM-05_53_13
Theory : continuity
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