Nuprl Lemma : fpf-single-dom-sq
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[x,y:A]. ∀[v:Top]. (x ∈ dom(y : v) ~ eq y x)
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-dom: x ∈ dom(f),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
fpf-single: x : v,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
deq: EqDecider(T)
Lemmas referenced :
deq_member_cons_lemma,
deq_member_nil_lemma,
bor-bfalse,
top_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
isectElimination,
applyEquality,
setElimination,
rename,
hypothesisEquality,
sqequalAxiom,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[x,y:A]. \mforall{}[v:Top]. (x \mmember{} dom(y : v) \msim{} eq y x)
Date html generated:
2018_05_21-PM-09_29_04
Last ObjectModification:
2018_02_09-AM-10_24_08
Theory : finite!partial!functions
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