Nuprl Lemma : fix_wf_partial
∀[A:Type]. ∀[f:partial(A) ⟶ partial(A)]. (fix(f) ∈ partial(A)) supposing value-type(A) ∧ mono(A)
Proof
Definitions occuring in Statement :
partial: partial(T),
mono: mono(T),
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
fix: fix(F),
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
fixpoint-induction-bottom2,
partial_wf,
bottom_wf-partial,
and_wf,
value-type_wf,
mono_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_isectElimination,
lambdaEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:partial(A) {}\mrightarrow{} partial(A)]. (fix(f) \mmember{} partial(A)) supposing value-type(A) \mwedge{} mono(A)
Date html generated:
2016_05_14-AM-06_10_13
Last ObjectModification:
2015_12_26-AM-11_51_58
Theory : partial_1
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