### Nuprl Lemma : le2-homogeneous

`∀[R:ℕ ⟶ ℕ ⟶ ℙ]. ∀[n:ℕ]. ∀[s:ℕn ⟶ ℕ].  ((n ≤ 2) `` strictly-increasing-seq(n;s) `` homogeneous(R;n;s))`

Proof

Definitions occuring in Statement :  homogeneous: `homogeneous(R;n;s)` strictly-increasing-seq: `strictly-increasing-seq(n;s)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` le: `A ≤ B` implies: `P `` Q` function: `x:A ⟶ B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` implies: `P `` Q` homogeneous: `homogeneous(R;n;s)` and: `P ∧ Q` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` int_seg: `{i..j-}` nat: `ℕ` le: `A ≤ B` member: `t ∈ T` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` rev_implies: `P `` Q` false: `False` prop: `ℙ` uiff: `uiff(P;Q)` uimplies: `b supposing a` lelt: `i ≤ j < k` subtype_rel: `A ⊆r B` top: `Top` less_than': `less_than'(a;b)` true: `True` sq_stable: `SqStable(P)` squash: `↓T`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation independent_pairFormation hypothesis cut sqequalHypSubstitution setElimination thin rename productElimination introduction extract_by_obid dependent_functionElimination hypothesisEquality unionElimination voidElimination independent_functionElimination independent_isectElimination isectElimination addEquality natural_numberEquality sqequalRule applyEquality lambdaEquality isect_memberEquality voidEquality intEquality because_Cache dependent_set_memberEquality imageMemberEquality baseClosed imageElimination equalityTransitivity equalitySymmetry setEquality hyp_replacement Error :applyLambdaEquality,  functionExtensionality functionEquality cumulativity universeEquality

Latex:
\mforall{}[R:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[n:\mBbbN{}].  \mforall{}[s:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}].
((n  \mleq{}  2)  {}\mRightarrow{}  strictly-increasing-seq(n;s)  {}\mRightarrow{}  homogeneous(R;n;s))

Date html generated: 2016_10_21-AM-09_37_56
Last ObjectModification: 2016_07_12-AM-05_01_09

Theory : bar-induction

Home Index