[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 63 from proof RG-restr-ok (previous step)

m0 < n, Guar(m0, cs, cs0), m0 ≤ m, CInv(n, act0, cs0), CInv(n, act, cs), m < n, ∀ m1. m1 ≠ m0 → (act0(m1) ↔ act(m1)) ∧ (Idle(m1, cs) ↔ Idle(m1, cs0)), (¬ act(m0) → Idle(m0, cs)) → ¬ act0(m0) → Idle(m0, cs0) ⊦ n = 0, Rely(m + 1, cs, cs0) ∧ (Idle(m + 1, cs) ↔ Idle(m + 1, cs0)) ∧ (act0(m + 1) ↔ act(m + 1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 64:
⊦ m ≠ n ∧ Guar(m, cs1, cs2) ∧ Inv(cs1) ∧ Inv(cs2) → (¬ Rely(n, cs1, cs2) ↔ false)
Proof step 65:
¬(m0 ≠ m + 1 ∧ Guar(m0, cs, cs0) ∧ Inv(cs) ∧ Inv(cs0)), m0 < n, Guar(m0, cs, cs0), m0 ≤ m, CInv(n, act0, cs0), CInv(n, act, cs), m < n, ∀ m1. m1 ≠ m0 → (act0(m1) ↔ act(m1)) ∧ (Idle(m1, cs) ↔ Idle(m1, cs0)), (¬ act(m0) → Idle(m0, cs)) → ¬ act0(m0) → Idle(m0, cs0) ⊦ n = 0, Rely(m + 1, cs, cs0) ∧ (Idle(m + 1, cs) ↔ Idle(m + 1, cs0)) ∧ (act0(m + 1) ↔ act(m + 1))
Proof step 73:
m0 ≠ m + 1 ∧ Guar(m0, cs, cs0) ∧ Inv(cs) ∧ Inv(cs0), m0 < n, Guar(m0, cs, cs0), m0 ≤ m, CInv(n, act0, cs0), CInv(n, act, cs), m < n, ∀ m1. m1 ≠ m0 → (act0(m1) ↔ act(m1)) ∧ (Idle(m1, cs) ↔ Idle(m1, cs0)), (¬ act(m0) → Idle(m0, cs)) → ¬ act0(m0) → Idle(m0, cs0) ⊦ n = 0, true ∧ (Idle(m + 1, cs) ↔ Idle(m + 1, cs0)) ∧ (act0(m + 1) ↔ act(m + 1))

Rule argument

spec: RGI-Conds inst: name: g-r seq: ⊦ m ≠ n ∧ Guar(m, cs1, cs2) ∧ Inv(cs1) ∧ Inv(cs2) → (¬ Rely(n, cs1, cs2) ↔ false) subst: [m, cs2, cs1, n] → [m0, cs0, cs, m + 1] flags: rewrite

Additional information

Used terms: m0, cs0, cs, m + 1