### Nuprl Lemma : sq_stable__bilinear_p

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

Proof

Definitions occuring in Statement :  bilinear_p: `IsBilinear(A;B;C;+a;+b;+c;f)` sq_stable: `SqStable(P)` uall: `∀[x:A]. B[x]` 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` so_lambda: `λ2x.t[x]` infix_ap: `x f y` so_apply: `x[s]` prop: `ℙ` implies: `P `` Q` sq_stable: `SqStable(P)` and: `P ∧ Q`
Lemmas referenced :  sq_stable__and uall_wf equal_wf infix_ap_wf sq_stable__uall sq_stable__equal squash_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis isect_memberEquality cumulativity because_Cache independent_functionElimination dependent_functionElimination axiomEquality lambdaFormation productElimination independent_pairEquality productEquality functionEquality 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].
SqStable(IsBilinear(A;B;C;+a;+b;+c;f))

Date html generated: 2016_05_15-PM-00_02_30
Last ObjectModification: 2015_12_26-PM-11_26_26

Theory : gen_algebra_1

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