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Proof step 15 from proof seq-sat-rg (previous step)

(Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S);Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S'))), 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 VD induction

And obtained the following new goals

Proof step 16:
(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 Boolvar, INDHYP-nat(N), GInv(S) ⊦ ((Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) ∧ ¬ Boolvar) -+-> (last ⊃ Po(m)(S) ∧ GInv(S);Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

Rule argument

indvar: (Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S) ∧ GInv(S) ;Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')) ) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: INDHYP-nat(N), (Ry(m)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Po(m)(S) ∧ GInv(S) ;Gr(m)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')) )