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Proof step 62 from proof rg2-lem1-term-unfair (previous step)

□ (N = N' ∧ ¬ N' < N''), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), ◇ Boolvar0, [:S | Boolvar0 ∨ Boolvar ::- [PL N = n16 ∧ N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)] ], INDHYP-nat(n16 + 1) ∧ INDHYP-nat0(n16 + 1), N = n16 + 1, Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, S) ⊦ ◇ last

User applied rule VD induction

And obtained the following new goals

Proof step 63:
[:S | Boolvar0 ∨ Boolvar ::- [PL N = n16 ∧ N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)] ], N0 = N0'' +1 until Boolvar0, □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), □ (N = N' ∧ ¬ N' < N''), (INDHYP-nat(n16 + 1) ∧ INDHYP-nat0(n16 + 1)) ∧ INDHYP-nat1(N0), N = n16 + 1, Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, S) ⊦ ◇ last

Rule argument

indvar: ◇ Boolvar0 wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: INDHYP-nat1(N0)