### Nuprl Lemma : sq_stable__bilinear

`∀[T:Type]. ∀[pl,tm:T ⟶ T ⟶ T].  SqStable(BiLinear(T;pl;tm))`

Proof

Definitions occuring in Statement :  bilinear: `BiLinear(T;pl;tm)` sq_stable: `SqStable(P)` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  bilinear: `BiLinear(T;pl;tm)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` prop: `ℙ` and: `P ∧ Q` infix_ap: `x f y` so_apply: `x[s]` implies: `P `` Q` sq_stable: `SqStable(P)`
Lemmas referenced :  sq_stable__uall uall_wf equal_wf infix_ap_wf sq_stable__and sq_stable__equal squash_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality cumulativity because_Cache productEquality functionExtensionality applyEquality hypothesis independent_functionElimination isect_memberEquality lambdaFormation dependent_functionElimination productElimination independent_pairEquality axiomEquality functionEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[pl,tm:T  {}\mrightarrow{}  T  {}\mrightarrow{}  T].    SqStable(BiLinear(T;pl;tm))

Date html generated: 2017_10_01-AM-08_12_54
Last ObjectModification: 2017_02_28-PM-01_57_32

Theory : gen_algebra_1

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