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Theorem step-L4-L0

⊦ ¬ ( ( ls.lspmx ≠ ∅ ∧ ( 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) = ls.lspmx) ∧ pre(gs, ls, L4, a) ∧ pcstepf(gs, ls, L4, a) = L0)

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: 2
Proof steps: 11
Used lemmas: disj-08, inj-03, elim-02, elim-03, pre-L4, disj-26, pcstepf-L4,
Used spec theorems:
- store/sparsearray/Extension
Used simplifier rules:
- tidset-npset/union-subset
- store/sparsearray/notmemlookup
- store/sparsearray/In-empty