Nuprl Lemma : fpf-restrict-domain
∀[f,P:Top]. (fpf-domain(fpf-restrict(f;P)) ~ filter(P;fpf-domain(f)))
Proof
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf-domain: fpf-domain(f),
filter: filter(P;l),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
domain_fpf_restrict_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[f,P:Top]. (fpf-domain(fpf-restrict(f;P)) \msim{} filter(P;fpf-domain(f)))
Date html generated:
2018_05_21-PM-09_31_16
Last ObjectModification:
2018_02_09-AM-10_25_42
Theory : finite!partial!functions
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