Nuprl Lemma : subtype-fpf-void
∀[A:Type]. ∀[B1:Top]. ∀[B2:A ⟶ Type]. (a:Void fp-> B1[a] ⊆r a:A fp-> B2[a])
Proof
Definitions occuring in Statement :
fpf: a:A fp-> B[a],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
function: x:A ⟶ B[x],
void: Void,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype-fpf3,
void_wf,
strong-subtype-void,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
voidEquality,
hypothesisEquality,
sqequalRule,
functionExtensionality,
voidElimination,
instantiate,
hypothesis,
lambdaEquality,
applyEquality,
independent_isectElimination,
lambdaFormation,
because_Cache,
axiomEquality,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B1:Top]. \mforall{}[B2:A {}\mrightarrow{} Type]. (a:Void fp-> B1[a] \msubseteq{}r a:A fp-> B2[a])
Date html generated:
2018_05_21-PM-09_17_09
Last ObjectModification:
2018_02_09-AM-10_16_24
Theory : finite!partial!functions
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