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Theorem rely-L2-L3

⊦ ls.tid ≠ tid0 ∧ ( ( alldisjointp(alltids, gs.ghostlspmxf) ∧ disjointp(U(alltids, gs.ghostlspmxf), gs.gspmx) ∧ gs.y + (U(alltids, gs.ghostlspmxf) ∪ gs.gspmx).toMatrix(gs.r, # gs.x) * gs.x = gs.spmx.toMatrix(gs.r, # gs.x) * gs.x ∧ U(alltids, gs.ghostlspmxf) ∪ gs.gspmx ⊆ gs.spmx ∧ # gs.y = gs.r ∧ okspmx(gs.spmx, gs.r, # gs.x)) ∧ gs.ghostlspmxf(ls.tid) = ∅) ∧ pre(gs, ls, L2, a) ∧ pcstepf(gs, ls, L2, a) = L3 → gs.ghostlspmxf(tid0) = gstepf(gs, ls, L2, a).ghostlspmxf(tid0) ∧ gstepf(gs, ls, L2, a).gspmx ⊆ gs.gspmx

Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 2
Used lemmas: updsel-26, updsel-30, updsel-14, updsel-11, gstepf-L2-1, updsel-54, disj-07, inj-04, pre-L2, disj-35, pcstepf-L2,
Used spec theorems:
- Used simplifier rules:
  - store+set/sparsearray/diff-subset
  - tidset-npset/union-subset