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Proof step 115 from proof rg2-lem2-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n22 ∧ S = s22 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s23 ∧ N = n23 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(n22 + 1) ∧ INDHYP-nat0(n2), R1(pm, s2, S), I(pm, s2), I(pm, s3), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), R1(pm, s3, S), R2(pm, s3, S), N ≤ n22 + 1, I(pm, s), G1(pm, s2, s2), R1(pm, s2, s22), G2(pm, s2, s3), R2(pm, s3, s23), n23 ≤ n22 + 1, R2(pm, s2, s2), R1(pm, s2, s3), I(pm, s22), I(pm, S), I(pm, s23), boolvar1 → s2 = s3 ∧ boolvar0 ∧ n2 = n4 ⊦ ◇ last

User applied rule cut formula

And obtained the following new goals

Proof step 116:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n22 ∧ S = s22 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s23 ∧ N = n23 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(n22 + 1) ∧ INDHYP-nat0(n2), R1(pm, s2, S), I(pm, s2), I(pm, s3), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), R1(pm, s3, S), R2(pm, s3, S), N ≤ n22 + 1, I(pm, s), G1(pm, s2, s2), R1(pm, s2, s22), G2(pm, s2, s3), R2(pm, s3, s23), n23 ≤ n22 + 1, R2(pm, s2, s2), R1(pm, s2, s3), I(pm, s22), I(pm, S), I(pm, s23), boolvar1 → s2 = s3 ∧ boolvar0 ∧ n2 = n4, N < n22 + 1 ⊦ ◇ last
Proof step 120:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n22 ∧ S = s22 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s23 ∧ N = n23 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(n22 + 1) ∧ INDHYP-nat0(n2), R1(pm, s2, S), I(pm, s2), I(pm, s3), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), R1(pm, s3, S), R2(pm, s3, S), N ≤ n22 + 1, I(pm, s), G1(pm, s2, s2), R1(pm, s2, s22), G2(pm, s2, s3), R2(pm, s3, s23), n23 ≤ n22 + 1, R2(pm, s2, s2), R1(pm, s2, s3), I(pm, s22), I(pm, S), I(pm, s23), boolvar1 → s2 = s3 ∧ boolvar0 ∧ n2 = n4, ¬ N < n22 + 1 ⊦ ◇ last

Rule argument

fma: N < n22 + 1

Additional information

Used formulas: N < n22 + 1