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Proof step 20 from proof not-pre1-term-unfair (previous step)

boolvar ∨ n = N + 1 ∧ N = N'' + 1 until Boolvar, [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s6 ∧ ¬ □ R2(pm, S', S'')]], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), INDHYP-nat(n + 1), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s1), Pre2(pm, s), R1(pm, s2, s3), R2(pm, s2, s3), G2(pm, s1, s2), R2(pm, s2, s5), R1(pm, s4, S), R2(pm, s4, S), R1(pm, s1, s2), I(pm, s5), I(pm, s2), I(pm, s1), I(pm, s3), Pre1(pm, s3), Pre1(pm, s2), I(pm, s), R1(pm, s1, s3), boolvar1 → s3 = s4 ∧ (boolvar ↔ boolvar0) ∧ n = n0, ¬ boolvar, s3 = s5, G2(pm, s5, s4), ¬ R2(pm, s4, s6), ¬ boolvar1 ⊦ ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
N = N'' + 1 until Boolvar, □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s6 ∧ ¬ □ R2(pm, S', S'')]], INDHYP-nat(2 + N), R1(pm, s1, s5), R1(pm, s1, S), R1(pm, s2, S), Pre1(pm, s5), R1(pm, s5, s4), G2(pm, s5, s4), I(pm, s), Pre1(pm, s2), I(pm, s1), I(pm, s2), I(pm, s5), R1(pm, s1, s2), R2(pm, s4, S), R1(pm, s4, S), G2(pm, s1, s2), R2(pm, s2, s5), R1(pm, s2, s5), Pre2(pm, s), Pre1(pm, s1), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, S), I(pm, s4), Pre1(pm, S), Pre1(pm, s4), R1(pm, s1, s4), R1(pm, s5, S), R1(pm, s2, s4), ¬ R2(pm, s4, s6) ⊦ ◇ last

Rule argument

Additional information

Used simplifier rules: r1-trans: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ R1(pm, s0, s1) ∧ I(pm, s) → R1(pm, s, s1);%r-g-r: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ G2(pm, s0, s1) ∧ R1(pm, s1, s2) ∧ I(pm, s) → R1(pm, s, s2);%pre1-r1: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ Pre1(pm, s) → Pre1(pm, s0);%g2-r1: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ G2(pm, s, s0) ∧ I(pm, s) → R1(pm, s, s0);%i-r1-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ I(pm, s) → I(pm, s0);%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2