Nuprl Lemma : iPO_wf

[K:dl_KripkeStructure]. ∀[s,t:worlds(K)].  (iPO(K;s;t) ∈ ℙ)


Proof




Definitions occuring in Statement :  dl_KripkeStructure: dl_KripkeStructure iPO: iPO(k;s;t) worlds: worlds(k) uall: [x:A]. B[x] prop: member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T dl_KripkeStructure: dl_KripkeStructure worlds: worlds(k) record+: record+ record-select: r.x subtype_rel: A ⊆B eq_atom: =a y ifthenelse: if then else fi  btrue: tt so_lambda: λ2x.t[x] so_apply: x[s] prop: iPO: iPO(k;s;t)
Lemmas referenced :  subtype_rel_self record-select_wf top_wf istype-atom nat_wf worlds_wf dl_KripkeStructure_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut sqequalHypSubstitution sqequalRule dependentIntersectionElimination dependentIntersectionEqElimination thin hypothesis applyEquality tokenEquality instantiate extract_by_obid isectElimination universeEquality functionEquality cumulativity lambdaEquality_alt equalityTransitivity equalitySymmetry hypothesisEquality axiomEquality inhabitedIsType isect_memberEquality_alt isectIsTypeImplies universeIsType

Latex:
\mforall{}[K:dl\_KripkeStructure].  \mforall{}[s,t:worlds(K)].    (iPO(K;s;t)  \mmember{}  \mBbbP{})



Date html generated: 2020_05_20-AM-09_01_14
Last ObjectModification: 2019_11_27-PM-02_15_13

Theory : dynamic!logic


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