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Proof step 69 from proof RG-restr-ok (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 70:
m0 < n, Guar(m0, cs, cs0), m0 ≤ m, CInv(n, act0, cs0), Inv(cs), m < n, ∀ m0. n < m0 → Idle(m0, cs) ∧ ¬ act(m0), m + 1 ≠ m0 → (act0(m + 1) ↔ act(m + 1)) ∧ (Idle(m + 1, cs) ↔ Idle(m + 1, cs0)), (¬ act(m0) → Idle(m0, cs)) → ¬ act0(m0) → Idle(m0, cs0) ⊦ n = 0, m0 = m + 1, Inv(cs0), Rely(m + 1, cs, cs0) ∧ (Idle(m + 1, cs) ↔ Idle(m + 1, cs0)) ∧ (act0(m + 1) ↔ act(m + 1))

Rule argument

pos: left 8 terms: m + 1 abort: F discard: T computed: T

Additional information

Used terms: m + 1