Nuprl Lemma : fix-diverges
∀f:partial(Void) ⟶ partial(Void). (fix(f) ~ ⊥)
Proof
Definitions occuring in Statement :
partial: partial(T),
bottom: ⊥,
all: ∀x:A. B[x],
fix: fix(F),
function: x:A ⟶ B[x],
void: Void,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
so_lambda: λ2x.t[x]
Lemmas referenced :
partial-void,
fixpoint-induction-bottom,
partial_wf,
void-value-type,
void-mono,
bottom_wf-partial
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
voidEquality,
hypothesis,
independent_isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}f:partial(Void) {}\mrightarrow{} partial(Void). (fix(f) \msim{} \mbot{})
Date html generated:
2016_05_14-AM-06_11_17
Last ObjectModification:
2015_12_26-AM-11_51_41
Theory : partial_1
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