Nuprl Lemma : fpf-accum_wf
∀[A,C:Type]. ∀[B:A ⟶ Type]. ∀[x:a:A fp-> B[a]]. ∀[y:C]. ∀[f:C ⟶ a:A ⟶ B[a] ⟶ C].
(fpf-accum(z,a,v.f[z;a;v];y;x) ∈ C)
Proof
Definitions occuring in Statement :
fpf-accum: fpf-accum(z,a,v.f[z; a; v];y;x),
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fpf: a:A fp-> B[a],
fpf-accum: fpf-accum(z,a,v.f[z; a; v];y;x),
pi2: snd(t),
pi1: fst(t),
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2]
Lemmas referenced :
fpf_wf,
list-subtype,
list_accum_wf,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
hypothesisEquality,
applyEquality,
isect_memberEquality,
isectElimination,
because_Cache,
lemma_by_obid,
lambdaEquality,
cumulativity,
universeEquality,
setEquality,
setElimination,
rename
Latex:
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x:a:A fp-> B[a]]. \mforall{}[y:C]. \mforall{}[f:C {}\mrightarrow{} a:A {}\mrightarrow{} B[a] {}\mrightarrow{} C].
(fpf-accum(z,a,v.f[z;a;v];y;x) \mmember{} C)
Date html generated:
2018_05_21-PM-09_26_35
Last ObjectModification:
2018_02_09-AM-10_22_00
Theory : finite!partial!functions
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