Nuprl Lemma : qoset_lt_irrefl
∀[s:QOSet]. ∀[a,b:|s|]. ¬(a = b ∈ |s|) supposing a <s b
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_lt: a <p b,
set_car: |p|,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
qoset: QOSet,
dset: DSet,
uiff: uiff(P;Q),
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
equal_wf,
set_car_wf,
set_lt_wf,
qoset_wf,
set_lt_is_sp_of_leq,
strict_part_irrefl,
set_leq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination
Latex:
\mforall{}[s:QOSet]. \mforall{}[a,b:|s|]. \mneg{}(a = b) supposing a <s b
Date html generated:
2017_10_01-AM-08_13_13
Last ObjectModification:
2017_02_28-PM-01_57_16
Theory : sets_1
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