Nuprl Lemma : mk_fpf_wf
∀[A:Type]. ∀[L:A List]. ∀[B:A ⟶ Type]. ∀[f:a:{a:A| (a ∈ L)} ⟶ B[a]]. (mk_fpf(L;f) ∈ a:A fp-> B[a])
Proof
Definitions occuring in Statement :
mk_fpf: mk_fpf(L;f),
fpf: a:A fp-> B[a],
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
mk_fpf: mk_fpf(L;f),
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
hypothesisEquality,
functionEquality,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[L:A List]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:\{a:A| (a \mmember{} L)\} {}\mrightarrow{} B[a]]. (mk\_fpf(L;f) \mmember{} a:A fp-> B[a\000C])
Date html generated:
2018_05_21-PM-09_24_35
Last ObjectModification:
2018_02_09-AM-10_20_29
Theory : finite!partial!functions
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