Nuprl Lemma : csm-state_wf
∀[V:Type]. ∀[sm:CSM(V)]. ∀[i:V]. ∀[L:(csm-aux(sm;i) × (Cmd(sm) + Msg(sm))) List]. (csm-state(sm;i;L) ∈ Type(sm;i))
Proof
Definitions occuring in Statement :
csm-state: csm-state(sm;i;L),
csm-aux: csm-aux(sm;i),
csm-type: Type(sm;i),
csm-msgtype: Msg(sm),
csm-cmd: Cmd(sm),
csm: CSM(V),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
csm-state: csm-state(sm;i;L),
spreadn: spread8,
csm: CSM(V),
csm-aux: csm-aux(sm;i),
pi2: snd(t),
pi1: fst(t),
csm-cmd: Cmd(sm),
csm-msgtype: Msg(sm),
csm-type: Type(sm;i),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_wf,
list_wf,
csm-aux_wf,
csm-cmd_wf,
csm-msgtype_wf,
csm_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
productEquality,
applyEquality,
hypothesisEquality,
unionEquality,
lambdaEquality,
spreadEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[V:Type]. \mforall{}[sm:CSM(V)]. \mforall{}[i:V]. \mforall{}[L:(csm-aux(sm;i) \mtimes{} (Cmd(sm) + Msg(sm))) List].
(csm-state(sm;i;L) \mmember{} Type(sm;i))
Date html generated:
2016_05_15-PM-05_11_18
Last ObjectModification:
2015_12_27-PM-02_23_01
Theory : general
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