Nuprl Lemma : phi-star_wf
∀[Phi:((ℕ ⟶ ℕ) ⟶ ℕ) ⟶ ℕ]. (Phi* ∈ ((ℕ ⟶ ℕ) ⟶ ℕ) ⟶ finite-nat-seq())
Proof
Definitions occuring in Statement :
phi-star: Phi*,
finite-nat-seq: finite-nat-seq(),
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,
phi-star: Phi*,
subtype_rel: A ⊆r B
Lemmas referenced :
nat_wf,
zero-seq_wf,
mk-finite-nat-seq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
because_Cache,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[Phi:((\mBbbN{} {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} \mBbbN{}]. (Phi* \mmember{} ((\mBbbN{} {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} finite-nat-seq())
Date html generated:
2016_05_14-PM-09_55_42
Last ObjectModification:
2016_01_15-AM-07_49_38
Theory : continuity
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