Nuprl Lemma : rel_rev_implies_weakening

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


Proof




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



Date html generated: 2016_05_14-AM-06_04_48
Last ObjectModification: 2015_12_26-AM-11_33_03

Theory : relations


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