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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