### Nuprl Lemma : rel_implies_weakening

`∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ].  (R1 `⇐⇒` R2 `` R1 => R2)`

Proof

Definitions occuring in Statement :  rel_equivalent: `R1 `⇐⇒` R2` rel_implies: `R1 => R2` uall: `∀[x:A]. B[x]` prop: `ℙ` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  rel_implies: `R1 => R2` rel_equivalent: `R1 `⇐⇒` R2` uall: `∀[x:A]. B[x]` implies: `P `` Q` all: `∀x:A. B[x]` member: `t ∈ T` iff: `P `⇐⇒` Q` and: `P ∧ Q` infix_ap: `x f y` 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{}[R1,R2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (R1  \mLeftarrow{}{}\mRightarrow{}  R2  {}\mRightarrow{}  R1  =>  R2)

Date html generated: 2016_05_14-AM-06_04_39
Last ObjectModification: 2015_12_26-AM-11_33_09

Theory : relations

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