Nuprl Lemma : Veldman-Ramsey
Ramsey's theorem -
infinite version has a constructive version here⋅
∀T:Type. ∀n:ℕ. ∀[R,S:n-aryRel(T)]. (almost-full(T;n;R) ⇒ almost-full(T;n;S) ⇒ almost-full(T;n;R ∧ S))
This theorem is one of freek's list of 100 theorems
Proof
Definitions occuring in Statement :
almost-full: almost-full(T;n;R),
nary-rel: n-aryRel(T),
prop_and: P ∧ Q,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
almost-full: almost-full(T;n;R),
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
nat: ℕ,
guard: {T},
or: P ∨ Q,
prop_and: P ∧ Q,
nary-rel: n-aryRel(T),
false: False,
and: P ∧ Q,
nary-rel-predicate: [[R]],
cand: A c∧ B
Lemmas referenced :
almost-full_wf,
nary-rel_wf,
nat_wf,
false_wf,
int_seg_wf,
tree-secures_functionality,
nary-rel-predicate_wf,
or_wf,
Veldman-Coquand,
and_wf,
tree-tensor_wf,
tree-secures_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
universeEquality,
lambdaEquality,
functionEquality,
natural_numberEquality,
setElimination,
rename,
dependent_functionElimination,
because_Cache,
sqequalRule,
applyEquality,
independent_functionElimination,
inrFormation,
dependent_pairFormation,
unionElimination,
voidElimination,
independent_pairFormation
Latex:
\mforall{}T:Type. \mforall{}n:\mBbbN{}.
\mforall{}[R,S:n-aryRel(T)]. (almost-full(T;n;R) {}\mRightarrow{} almost-full(T;n;S) {}\mRightarrow{} almost-full(T;n;R \mwedge{} S))
Date html generated:
2016_07_08-PM-04_49_44
Last ObjectModification:
2015_12_26-PM-07_54_56
Theory : fan-theorem
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