Nuprl Lemma : no_repeats-pairs-fpf
∀[A,B:Type]. ∀[eq1:EqDecider(A)]. ∀[eq2:EqDecider(B)]. ∀[L:(A × B) List]. no_repeats(A;fpf-domain(fpf(L)))
Proof
Definitions occuring in Statement :
pairs-fpf: fpf(L),
fpf-domain: fpf-domain(f),
no_repeats: no_repeats(T;l),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
implies: P ⇒ Q
Lemmas referenced :
pairs-fpf_property,
no_repeats_witness,
fpf-domain_wf,
pairs-fpf_wf,
subtype-fpf2,
list_wf,
top_wf,
deq_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
dependent_functionElimination,
productElimination,
applyEquality,
because_Cache,
sqequalRule,
lambdaEquality,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
independent_functionElimination,
productEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[eq1:EqDecider(A)]. \mforall{}[eq2:EqDecider(B)]. \mforall{}[L:(A \mtimes{} B) List].
no\_repeats(A;fpf-domain(fpf(L)))
Date html generated:
2018_05_21-PM-09_32_04
Last ObjectModification:
2018_02_09-AM-10_26_50
Theory : finite!partial!functions
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