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Theorem rely-PROP_W

⊦ ( ctrok(gs.fctr, gs.fwriters) ∧ writersOk(gs.bq, gs.pq, gs.fwriters) ∧ pendingOk(gs.bq, gs.pq) ∧ SFTrailing(gs.bq) ∧ readFOsOk(gs.rfo, gs.fwriters)) ∧ (gs.bq(tid) ≠ [] ∧ gs.bq(tid).head.W?) ∧ gs0 = (gs.pq:= gs.pq(gs.bq(tid).head.l := gs.pq(gs.bq(tid).head.l) + W(gs.bq(tid).head.v, tid))).bq:= gs.bq(tid := gs.bq(tid).tail) → (∀ t0. relyws(t0, gs.freaders, gs0.freaders) ∧ relyws(t0, gs.fwriters, gs0.fwriters) ∧ rely(t0, gs.pq, gs.bq, gs0.pq, gs0.bq) ∧ gs.bq(t0) ⊒w gs0.bq(t0) ∧ (gs.rfo(t0) = [] → gs0.rfo(t0) = []) ∧ (gs.rfo(t0) = gs.bq(t0) → gs0.rfo(t0) = gs0.bq(t0)) ∧ (gs.rfo(t0) + SF ' = gs.bq(t0) → gs0.rfo(t0) + SF ' = gs0.bq(t0) ∨ gs0.rfo(t0) = gs0.bq(t0)))

Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by: FLITInv-thm, other-FLITLInv, rely-FLITLInv, stable-FLITLInv, step-FLITLInv,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 15
Used lemmas:
Used spec theorems:
- list-last/splitlasteq
Used simplifier rules: