### Nuprl Lemma : rel_implies_functionality

`∀[T:Type]. ∀[A1,A2,B1,B2:T ⟶ T ⟶ ℙ].  (A1 `` A2 `` B1 => B2 `` {A1 => B1 `` A2 => B2})`

Proof

Definitions occuring in Statement :  rel_rev_implies: `R1 `` R2` rel_implies: `R1 => R2` uall: `∀[x:A]. B[x]` prop: `ℙ` guard: `{T}` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  rel_implies: `R1 => R2` guard: `{T}` rel_rev_implies: `R1 `` R2` uall: `∀[x:A]. B[x]` implies: `P `` Q` all: `∀x:A. B[x]` member: `t ∈ T` prop: `ℙ` infix_ap: `x f y` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  all_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation applyEquality hypothesisEquality cut lemma_by_obid sqequalHypSubstitution isectElimination thin lambdaEquality functionEquality hypothesis cumulativity universeEquality dependent_functionElimination independent_functionElimination

Latex:
\mforall{}[T:Type].  \mforall{}[A1,A2,B1,B2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (A1  \mLeftarrow{}{}  A2  {}\mRightarrow{}  B1  =>  B2  {}\mRightarrow{}  \{A1  =>  B1  {}\mRightarrow{}  A2  =>  B2\})

Date html generated: 2016_05_14-AM-06_04_50
Last ObjectModification: 2015_12_26-AM-11_33_04

Theory : relations

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