Nuprl Lemma : fpf-cap-subtype_functionality
∀[A:Type]. ∀[d1,d2:EqDecider(A)]. ∀[f:a:A fp-> Type]. ∀[x:A]. ∀[z:Type]. (f(x)?z ⊆r f(x)?z)
Proof
Definitions occuring in Statement :
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
subtype_rel: A ⊆r B,
uall: ∀[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],
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel-equal,
fpf-cap_wf,
fpf-cap_functionality,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
universeEquality,
hypothesis,
independent_isectElimination,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[d1,d2:EqDecider(A)]. \mforall{}[f:a:A fp-> Type]. \mforall{}[x:A]. \mforall{}[z:Type]. (f(x)?z \msubseteq{}r f(x)?z)
Date html generated:
2018_05_21-PM-09_19_33
Last ObjectModification:
2018_02_09-AM-10_17_39
Theory : finite!partial!functions
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