### Nuprl Lemma : binrel_le_weakening

`∀[T:Type]. ∀[R,R':T ⟶ T ⟶ ℙ].  ((R <≡>{T} R') `` (R ≡>{T} R'))`

Proof

Definitions occuring in Statement :  binrel_le: `E ≡>{T} E'` binrel_eqv: `E <≡>{T} E'` uall: `∀[x:A]. B[x]` prop: `ℙ` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  binrel_le: `E ≡>{T} E'` binrel_eqv: `E <≡>{T} E'` uall: `∀[x:A]. B[x]` implies: `P `` Q` all: `∀x:A. B[x]` member: `t ∈ T` iff: `P `⇐⇒` Q` and: `P ∧ Q` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  all_wf iff_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation cut hypothesis sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality productElimination independent_functionElimination applyEquality lemma_by_obid isectElimination lambdaEquality functionEquality cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R,R':T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    ((R  <\mequiv{}>\{T\}  R')  {}\mRightarrow{}  (R  \mequiv{}>\{T\}  R'))

Date html generated: 2016_05_14-PM-03_54_56
Last ObjectModification: 2015_12_26-PM-06_55_49

Theory : relations2

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