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Theorem labs-def

⊦ labs(gs, ls, pc, ags, als, apc) ↔ ls.tid = als.tid ∧ (pc = idle → apc = idle) ∧ (pc = I1 ∨ pc = I2 ∨ pc = I3 ∨ pc = I4 ∨ pc = I6 ∨ pc = I10 ∨ pc = I11 ∨ pc = I12 ∨ pc = I16 ∨ pc = I17 ∨ pc = I18 ∨ pc = I20 → apc = invInsert) ∧ (pc = I5 → apc = (ls.b ⊃ retInsert;invInsert)) ∧ (pc = I7 ∨ pc = I13 → apc = (ls.e = ls.e0 ⊃ retInsert;invInsert)) ∧ (pc = I8 → apc = retInsert) ∧ (pc = I9 ∨ pc = I14 ∨ pc = I15 ∨ pc = I19 ∨ pc = I21 → apc = retInsert) ∧ (pc = I7 ∨ pc = I8 ∨ pc = I13 ∨ pc = I14 → ls.e = ls.e0 → als.lb) ∧ (pc = I9 ∨ pc = I15 ∨ pc = I19 → (als.lb ↔ ls.b)) ∧ (pc = I5 → ls.b → ¬ als.lb) ∧ (pc = I21 → ¬ als.lb) ∧ (pc = M1 ∨ pc = M2 ∨ pc = M3 ∨ pc = M4 ∨ pc = M5 ∨ pc = M6 ∨ pc = M17 → apc = invMember) ∧ (pc = M7 → apc = (ls.e0 ≠ ls.e ∧ ls.e0 ≠ ⊥ ∧ (ls.n + 1) % # gs.ar ≠ ls.n0 ⊃ invMember;retMember)) ∧ (pc = M10 → apc = (ls.e0 ≠ ⊥ ∧ (ls.n + 1) % # gs.ar ≠ ls.n0 ⊃ invMember;retMember)) ∧ (pc = M13 → apc = ((ls.n + 1) % # gs.ar ≠ ls.n0 ⊃ invMember;retMember)) ∧ (pc = M14 → apc = (ls.n ≠ ls.n0 ⊃ invMember;retMember)) ∧ (pc = M8 ∨ pc = M9 ∨ pc = M11 ∨ pc = M12 ∨ pc = M15 ∨ pc = M16 → apc = retMember) ∧ (pc = M7 → ls.e0 = ls.e ∨ ls.e0 = ⊥ ∨ (ls.n + 1) % # gs.ar = ls.n0 → (ls.e = ls.e0 ↔ als.lb)) ∧ (pc = M10 → ls.e0 = ⊥ ∨ (ls.n + 1) % # gs.ar = ls.n0 → ¬ als.lb) ∧ (pc = M13 → (ls.n + 1) % # gs.ar = ls.n0 → ¬ als.lb) ∧ (pc = M14 → ls.n = ls.n0 → ¬ als.lb) ∧ (pc = M9 ∨ pc = M12 ∨ pc = M16 → (als.lb ↔ ls.b)) ∧ (pc = M11 ∨ pc = M15 → ¬ als.lb) ∧ (pc = M8 → als.lb) ∧ (apc = invMember ∨ apc = invInsert → ls.e = als.le)