Nuprl Lemma : fpf-dom_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f:a:A fp-> Top]. ∀[x:A]. (x ∈ dom(f) ∈ 𝔹)
Proof
Definitions occuring in Statement :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
deq-member_wf,
pi1_wf_top,
list_wf,
subtype_rel_product,
l_member_wf,
top_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
functionEquality,
setEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:a:A fp-> Top]. \mforall{}[x:A]. (x \mmember{} dom(f) \mmember{} \mBbbB{})
Date html generated:
2018_05_21-PM-09_17_11
Last ObjectModification:
2018_02_09-AM-10_16_25
Theory : finite!partial!functions
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