Nuprl Lemma : domain_fpf_restrict_lemma
∀P,f: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),
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
fpf-restrict: fpf-restrict(f;P),
fpf-domain: fpf-domain(f),
mk_fpf: mk_fpf(L;f),
pi1: fst(t)
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule
Latex:
\mforall{}P,f:Top. (fpf-domain(fpf-restrict(f;P)) \msim{} filter(P;fpf-domain(f)))
Date html generated:
2018_05_21-PM-09_31_09
Last ObjectModification:
2018_02_09-AM-10_25_33
Theory : finite!partial!functions
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