Nuprl Lemma : wellfounded-anti-reflexive
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[a:T]. (¬R[a;a]) supposing WellFnd{i}(T;x,y.R[x;y])
Proof
Definitions occuring in Statement :
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
not: ¬A,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y]
Lemmas referenced :
not_wf,
all_wf,
wellfounded_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
lambdaEquality,
lemma_by_obid,
applyEquality,
hypothesisEquality,
independent_functionElimination,
functionEquality,
because_Cache,
dependent_functionElimination,
voidElimination,
universeEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[a:T]. (\mneg{}R[a;a]) supposing WellFnd\{i\}(T;x,y.R[x;y])
Date html generated:
2016_05_15-PM-03_56_16
Last ObjectModification:
2015_12_27-PM-03_09_10
Theory : general
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