Nuprl Lemma : setmem-irreflexive
∀s:Set{i:l}. (¬(s ∈ s))
Proof
Definitions occuring in Statement :
Set: Set{i:l},
setmem: (x ∈ s),
all: ∀x:A. B[x],
not: ¬A
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
exists: ∃x:A. B[x],
top: Top,
false: False,
not: ¬A,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
member: t ∈ T,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x]
Lemmas referenced :
seteq_wf,
seteq_weakening,
seteq-iff,
setmem-iff,
item_mk_set_lemma,
dom_mk_set_lemma,
all_wf,
mk-set_wf,
Set_wf,
set-subtype-coSet,
setmem_wf,
not_wf,
set-induction
Rules used in proof :
dependent_pairFormation,
productElimination,
voidEquality,
isect_memberEquality,
dependent_functionElimination,
functionEquality,
voidElimination,
lambdaFormation,
independent_functionElimination,
because_Cache,
hypothesis,
applyEquality,
hypothesisEquality,
cumulativity,
lambdaEquality,
sqequalRule,
thin,
isectElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}s:Set\{i:l\}. (\mneg{}(s \mmember{} s))
Date html generated:
2018_07_29-AM-09_51_51
Last ObjectModification:
2018_07_11-PM-03_36_19
Theory : constructive!set!theory
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