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Proof step 18 from proof seq-sat-rg-total-lem (previous step)

(Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S);Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S'))), N = N'' + 1 until last, INDHYP-nat(N + 1), GInv(S), Ry(m)(s0, S), GInv(s0), Gr(m)(s, s0), GInv(s) ⊦ (Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S) ∧ GInv(S);Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

User applied rule apply VD induction

And closed the goal!

Rule argument

subst: [m] → [m] path: 1, 2, 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