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: implies:  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:  Q all: x:A. B[x] member: t ∈ T iff: ⇐⇒ Q and: P ∧ Q prop: 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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