Nuprl Lemma : fpf-type
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:a:A fp-> B[a]]. (f ∈ a:{a:A| (a ∈ fpf-domain(f))} fp-> B[a])
Proof
Definitions occuring in Statement :
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fpf: a:A fp-> B[a],
so_lambda: λ2x.t[x],
so_apply: x[s],
fpf-domain: fpf-domain(f),
pi1: fst(t),
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a
Lemmas referenced :
fpf_wf,
list-subtype,
subtype_rel_dep_function,
l_member_wf,
set_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality,
productElimination,
dependent_pairEquality,
setEquality,
setElimination,
rename,
lambdaFormation,
dependent_set_memberEquality,
independent_isectElimination
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. (f \mmember{} a:\{a:A| (a \mmember{} fpf-domain(f))\} fp-> B[a])
Date html generated:
2018_05_21-PM-09_17_28
Last ObjectModification:
2018_02_09-AM-10_16_31
Theory : finite!partial!functions
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