Nuprl Lemma : fpf-dom-list_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f:a:A fp-> Top]. (fpf-dom-list(f) ∈ {a:A| ↑a ∈ dom(f)} List)
Proof
Definitions occuring in Statement :
fpf-dom-list: fpf-dom-list(f),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
list: T List,
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
set: {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-dom-list: fpf-dom-list(f),
fpf-dom: x ∈ dom(f),
pi1: fst(t),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list-set-type,
subtype_rel_list_set,
l_member_wf,
assert_wf,
deq-member_wf,
assert-deq-member,
fpf_wf,
top_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
applyEquality,
because_Cache,
lambdaEquality,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:a:A fp-> Top]. (fpf-dom-list(f) \mmember{} \{a:A| \muparrow{}a \mmember{} dom(f)\} List)
Date html generated:
2018_05_21-PM-09_30_49
Last ObjectModification:
2018_02_09-AM-10_25_17
Theory : finite!partial!functions
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