Nuprl Lemma : fpf-single-sub-reflexive
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[x:A]. ∀[v:B[x]]. ∀[eqa:EqDecider(A)]. x : v ⊆ x : v
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-sub: f ⊆ g,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
uimplies: b supposing a
Lemmas referenced :
fpf-sub_witness,
fpf-single_wf,
deq_wf,
fpf-sub_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
instantiate,
hypothesis,
because_Cache,
independent_functionElimination,
isect_memberEquality,
functionEquality,
cumulativity,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x:A]. \mforall{}[v:B[x]]. \mforall{}[eqa:EqDecider(A)]. x : v \msubseteq{} x : v
Date html generated:
2018_05_21-PM-09_24_43
Last ObjectModification:
2018_02_09-AM-10_20_42
Theory : finite!partial!functions
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