[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 26 from proof COP-sat-rely-guar (previous step)

N = N'' + 1 until Boolvar, (Rely(m, CS', CS'') ∧ (Idle(m, CS') ↔ Idle(m, CS'')) ∧ (Inv(CS') → Inv(CS''))) -+-> (last ⊃ Idle(m, CS) ∧ Inv(CS);Guar(m, CS, CS') ∧ (∀ m0. m0 ≠ m → (Idle(m0, CS) ↔ Idle(m0, CS'))) ∧ (Inv(CS) → Inv(CS'))), □ (Act = Act' ∧ Inp = Inp'), INDHYP-nat(N + 1), Act(m), CInv(n, Act, CS), CRely(m, act0, cs0, Act, CS), CInv(n, act0, cs0), Guar(m, cs, cs0), m ≤ n, act0(m), CInv(n, act0, cs), boolvar1 → cs = cs0 ∧ ¬ boolvar0 ∧ N + 1 = n1, Inv(cs) → Inv(cs0), ∀ m1. m1 ≠ m → (Idle(m1, cs) ↔ Idle(m1, cs0)) ⊦ (CRely(m, Act', CS', Act'', CS'') ∧ (CInv(n, Act', CS') ∧ Act'(m) → CInv(n, Act'', CS'') ∧ Act''(m)) ∧ ¬ Boolvar) -+-> (last ⊃ CInv(n, Act, CS) ∧ Idle(m, CS) ∧ Act(m);CGuar(m, Act, CS, Act', CS') ∧ (CInv(n, Act, CS) ∧ Act(m) → CInv(n, Act', CS') ∧ Act'(m)))

User applied rule apply VD induction

And closed the goal!

Rule argument

subst: [m, n] → [m, n] path: 1, 1, 1, 1, 2, 1, 1

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: m, n