Nuprl Lemma : homogeneous_wf
∀[R:ℕ ⟶ ℕ ⟶ ℙ]. ∀[n:ℕ]. ∀[s:ℕn ⟶ ℕ]. (homogeneous(R;n;s) ∈ ℙ)
Proof
Definitions occuring in Statement :
homogeneous: homogeneous(R;n;s),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
homogeneous: homogeneous(R;n;s),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int_seg: {i..j-},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
strictly-increasing-seq_wf,
subtype_rel_dep_function,
int_seg_wf,
nat_wf,
all_wf,
less_than_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
natural_numberEquality,
setElimination,
rename,
hypothesis,
lambdaEquality,
because_Cache,
intEquality,
independent_isectElimination,
lambdaFormation,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[R:\mBbbN{} {}\mrightarrow{} \mBbbN{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:\mBbbN{}n {}\mrightarrow{} \mBbbN{}]. (homogeneous(R;n;s) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_50_04
Last ObjectModification:
2015_12_26-AM-10_17_32
Theory : bar-induction
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