Nuprl Lemma : fpf-add-single_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[x:A]. ∀[v:B[x]]. ∀[eq:EqDecider(A)]. ∀[f:x:A fp-> B[x]]. (fx : v ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-add-single: fpf-add-single,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-add-single: fpf-add-single,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fpf-join_wf,
fpf-single_wf,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
instantiate,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x:A]. \mforall{}[v:B[x]]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:x:A fp-> B[x]].
(f
x : v \mmember{} x:A fp-> B[x])
Date html generated:
2018_05_21-PM-09_25_25
Last ObjectModification:
2018_02_09-AM-10_21_22
Theory : finite!partial!functions
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