Nuprl Lemma : fpf-dom-type2
∀[X,Y:Type]. ∀[eq:EqDecider(Y)]. ∀[f:x:X fp-> Top]. ∀[x:Y]. {x ∈ X supposing ↑x ∈ dom(f)} supposing strong-subtype(X;Y)
Proof
Definitions occuring in Statement :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
strong-subtype: strong-subtype(A;B),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
guard: {T},
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
guard: {T}
Lemmas referenced :
fpf-dom-type
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
hypothesis
Latex:
\mforall{}[X,Y:Type]. \mforall{}[eq:EqDecider(Y)]. \mforall{}[f:x:X fp-> Top]. \mforall{}[x:Y].
\{x \mmember{} X supposing \muparrow{}x \mmember{} dom(f)\} supposing strong-subtype(X;Y)
Date html generated:
2018_05_21-PM-09_17_34
Last ObjectModification:
2018_02_09-AM-10_16_34
Theory : finite!partial!functions
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