Nuprl Lemma : fset-image-empty
∀[eqt,eqa,f:Top]. (f"({}) ~ {})
Proof
Definitions occuring in Statement :
fset-image: f"(s),
empty-fset: {},
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
empty-fset: {},
fset-image: f"(s),
f-union: f-union(domeq;rngeq;s;x.g[x]),
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[eqt,eqa,f:Top]. (f"(\{\}) \msim{} \{\})
Date html generated:
2016_05_14-PM-03_43_55
Last ObjectModification:
2015_12_26-PM-06_38_49
Theory : finite!sets
Home
Index