Nuprl Lemma : fpf-dom_functionality2
∀[A:Type]. ∀[eq1,eq2:EqDecider(A)]. ∀[f:a:A fp-> Top]. ∀[x:A]. {↑x ∈ dom(f) supposing ↑x ∈ dom(f)}
Proof
Definitions occuring in Statement :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
guard: {T},
universe: Type
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
fpf-dom_functionality,
top_wf,
assert_wf,
assert_witness,
fpf-dom_wf,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
lambdaEquality,
hypothesis,
cumulativity,
hypothesisEquality,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq1,eq2:EqDecider(A)]. \mforall{}[f:a:A fp-> Top]. \mforall{}[x:A]. \{\muparrow{}x \mmember{} dom(f) supposing \muparrow{}x \mmember{} dom(f)\}
Date html generated:
2018_05_21-PM-09_17_31
Last ObjectModification:
2018_02_09-AM-10_16_33
Theory : finite!partial!functions
Home
Index