Nuprl Lemma : fpf-contains_self
∀[A:Type]. ∀[B:A ⟶ Type]. ∀eq:EqDecider(A). ∀f:a:A fp-> B[a] List. f ⊆⊆ f
Proof
Definitions occuring in Statement :
fpf-contains: f ⊆⊆ g,
fpf: a:A fp-> B[a],
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-contains: f ⊆⊆ g,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B,
member: t ∈ T,
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
l_contains_weakening,
fpf-ap_wf,
list_wf,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
hypothesis,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
dependent_functionElimination,
lambdaEquality,
independent_isectElimination,
because_Cache,
isect_memberEquality,
voidElimination,
voidEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}eq:EqDecider(A). \mforall{}f:a:A fp-> B[a] List. f \msubseteq{}\msubseteq{} f
Date html generated:
2018_05_21-PM-09_19_15
Last ObjectModification:
2018_02_09-AM-10_17_29
Theory : finite!partial!functions
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