### Nuprl Lemma : bilinear_p_wf

`∀[A,B,C:Type]. ∀[+a:A ⟶ A ⟶ A]. ∀[+b:B ⟶ B ⟶ B]. ∀[+c:C ⟶ C ⟶ C]. ∀[f:A ⟶ B ⟶ C].`
`  (IsBilinear(A;B;C;+a;+b;+c;f) ∈ ℙ)`

Proof

Definitions occuring in Statement :  bilinear_p: `IsBilinear(A;B;C;+a;+b;+c;f)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  bilinear_p: `IsBilinear(A;B;C;+a;+b;+c;f)` uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ` and: `P ∧ Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` infix_ap: `x f y`
Lemmas referenced :  uall_wf equal_wf infix_ap_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut productEquality lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality lambdaEquality because_Cache hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality universeEquality

Latex:
\mforall{}[A,B,C:Type].  \mforall{}[+a:A  {}\mrightarrow{}  A  {}\mrightarrow{}  A].  \mforall{}[+b:B  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[+c:C  {}\mrightarrow{}  C  {}\mrightarrow{}  C].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  C].
(IsBilinear(A;B;C;+a;+b;+c;f)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-00_02_28
Last ObjectModification: 2015_12_26-PM-11_25_44

Theory : gen_algebra_1

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