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Theorem step-L4-L5

⊦ ( 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) = L5 → lstepf(gs, ls, L4, a).np ∈ lstepf(gs, ls, L4, a).lspmx ∧ ( alldisjointp(alltids, gstepf(gs, ls, L4, a).ghostlspmxf) ∧ disjointp(U(alltids, gstepf(gs, ls, L4, a).ghostlspmxf), gstepf(gs, ls, L4, a).gspmx) ∧ gstepf(gs, ls, L4, a).y + (U(alltids, gstepf(gs, ls, L4, a).ghostlspmxf) ∪ gstepf(gs, ls, L4, a).gspmx ).toMatrix (gstepf(gs, ls, L4, a).r, # gstepf(gs, ls, L4, a).x ) * gstepf(gs, ls, L4, a).x = gstepf(gs, ls, L4, a).spmx.toMatrix(gstepf(gs, ls, L4, a).r, # gstepf(gs, ls, L4, a).x) * gstepf(gs, ls, L4, a).x ∧ U(alltids, gstepf(gs, ls, L4, a).ghostlspmxf) ∪ gstepf(gs, ls, L4, a).gspmx ⊆ gstepf(gs, ls, L4, a).spmx ∧ # gstepf(gs, ls, L4, a).y = gstepf(gs, ls, L4, a).r ∧ okspmx(gstepf(gs, ls, L4, a).spmx, gstepf(gs, ls, L4, a).r, # gstepf(gs, ls, L4, a).x)) ∧ gstepf(gs, ls, L4, a).ghostlspmxf(lstepf(gs, ls, L4, a).tid) = lstepf(gs, ls, L4, a).lspmx

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