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Theorem plibStep

⊦ plibStep(mkstate(gs, lsf, pcf), a, mkstate(gs0, lsf0, pcf0)) ↔ (∃ t, ls, pc. lstep(gs, lsf(t), pcf(t), a, gs0, ls, pc) ∧ lsf0 = lsf(t := ls) ∧ pcf0 = pcf(t := pc)) ∨ a = globalACrash ∧ ⟨pm := gs.pm, vm := gs.vm, h := gs.h; ACrash(pm; vm, h, pcf); gs := (gs.vm:= vm).h:= h⟩ (gs0 = gs ∧ lsf0 = lsf ∧ pcf0 = pcf) ∨ (∃ l. a = globalAPersist(l) ∧ firstVolWrite(l, gs.h) < # gs.h ∧ gs0 = (gs.pm:= gs.pm(l := gs.h[firstVolWrite(l, gs.h)]._1.v)) .h:= ( gs.h.take(firstVolWrite(l, gs.h)) + ((gs.h[firstVolWrite(l, gs.h)]._1, true) + persistDependentReads(l, gs.h.drop(firstVolWrite(l, gs.h) + 1)))) ∧ lsf0 = lsf ∧ pcf0 = pcf)