Nuprl Lemma : convolution_wf
∀[A,B,C:Type]. ∀[f:A ⟶ B ⟶ C ⟶ C]. ∀[c0:C]. ∀[L1:A List]. ∀[L2:B List]. (convolution(a,b,c.f[a;b;c];c0;L1;L2) ∈ C)
Proof
Definitions occuring in Statement :
convolution: convolution(a,b,c.f[a; b; c];c0;L1;L2),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
convolution: convolution(a,b,c.f[a; b; c];c0;L1;L2),
so_lambda: λ2x y.t[x; y],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
cps-accum_wf,
list_wf,
list_ind_wf,
pi2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productEquality,
hypothesis,
lambdaEquality,
spreadEquality,
independent_pairEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} C {}\mrightarrow{} C]. \mforall{}[c0:C]. \mforall{}[L1:A List]. \mforall{}[L2:B List].
(convolution(a,b,c.f[a;b;c];c0;L1;L2) \mmember{} C)
Date html generated:
2016_05_15-PM-03_48_37
Last ObjectModification:
2015_12_27-PM-01_21_34
Theory : general
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