Nuprl Lemma : min-inc-seq_wf
∀[a:ℕ ⟶ ℕ]. ∀[n,k:ℕ]. (min-inc-seq(a;n;k) ∈ ℕ)
Proof
Definitions occuring in Statement :
min-inc-seq: min-inc-seq(a;n;k),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
min-inc-seq: min-inc-seq(a;n;k),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
min-increasing-sequence_wf,
nat_wf,
unit_wf2,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
unionEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
functionEquality
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[n,k:\mBbbN{}]. (min-inc-seq(a;n;k) \mmember{} \mBbbN{})
Date html generated:
2019_06_20-PM-03_07_17
Last ObjectModification:
2018_08_21-PM-01_57_20
Theory : continuity
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