Nuprl Lemma : fset-union-empty
∀[eq,s:Top]. (s ⋃ {} ~ s)
Proof
Definitions occuring in Statement :
empty-fset: {},
fset-union: x ⋃ y,
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-union: x ⋃ y,
l-union: as ⋃ bs,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
reduce_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{}[eq,s:Top]. (s \mcup{} \{\} \msim{} s)
Date html generated:
2016_05_14-PM-03_40_46
Last ObjectModification:
2015_12_26-PM-06_40_42
Theory : finite!sets
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