Nuprl Lemma : fset-image-singleton
∀[eqt,eqa,f,x:Top]. (f"({x}) ~ {f x})
Proof
Definitions occuring in Statement :
fset-image: f"(s),
fset-singleton: {x},
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset-singleton: {x},
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],
fset-union: x ⋃ y,
l-union: as ⋃ bs
Lemmas referenced :
list_accum_cons_lemma,
list_accum_nil_lemma,
reduce_cons_lemma,
reduce_nil_lemma,
insert_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,x:Top]. (f"(\{x\}) \msim{} \{f x\})
Date html generated:
2016_05_14-PM-03_43_52
Last ObjectModification:
2015_12_26-PM-06_39_00
Theory : finite!sets
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