Nuprl Lemma : strict-fun
∀[f:Base]. f ∈ partial(Void) ⟶ partial(Void) supposing f ⊥ ~ ⊥
Proof
Definitions occuring in Statement :
partial: partial(T),
bottom: ⊥,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
base: Base,
void: Void,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
partial-void,
bottom_wf-partial,
void-value-type,
partial_wf,
base_sq,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isectElimination,
voidEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
sqequalIntensionalEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[f:Base]. f \mmember{} partial(Void) {}\mrightarrow{} partial(Void) supposing f \mbot{} \msim{} \mbot{}
Date html generated:
2016_05_14-AM-06_11_19
Last ObjectModification:
2015_12_26-AM-11_51_44
Theory : partial_1
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