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Theorem stable-L7-01

⊦ ( ( ( 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)) ∧ ls.np ∈ ls.lspmx ∧ gs.ghostlspmxf(ls.tid) = ls.lspmx -- ls.np) ∧ alldisjointp(alltids, gs0.ghostlspmxf) ∧ disjointp(U(alltids, gs0.ghostlspmxf), gs0.gspmx) ∧ gs0.y + (U(alltids, gs0.ghostlspmxf) ∪ gs0.gspmx).toMatrix(gs0.r, # gs0.x) * gs0.x = gs0.spmx.toMatrix(gs0.r, # gs0.x) * gs0.x ∧ U(alltids, gs0.ghostlspmxf) ∪ gs0.gspmx ⊆ gs0.spmx ∧ # gs0.y = gs0.r ∧ okspmx(gs0.spmx, gs0.r, # gs0.x)) ∧ gs.ghostlspmxf(ls.tid) = gs0.ghostlspmxf(ls.tid) ∧ gs0.gspmx ⊆ gs.gspmx → ls.np ∈ ls.lspmx ∧ gs0.ghostlspmxf(ls.tid) = ls.lspmx -- ls.np

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

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Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 2
Used lemmas:
Used spec theorems:
- Used simplifier rules:
  - store/sparsearray/sub-trans
  - tidset-npset/union-subset