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Proof step 23 from proof not-pre1-term-unfair (previous step)

[:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s7 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ¬ □ R2(pm, S', S'')]], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), N = N'' + 1 until Boolvar, INDHYP-nat(2 + N), R1(pm, s2, s4), R1(pm, s5, S), R1(pm, s1, s4), Pre1(pm, s4), Pre1(pm, S), I(pm, s4), I(pm, S), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s1), Pre2(pm, s), R1(pm, s2, s5), G2(pm, s1, s2), R2(pm, s2, s5), R1(pm, s4, S), R2(pm, s4, S), R1(pm, s1, s2), I(pm, s2), I(pm, s1), I(pm, s5), Pre1(pm, s2), I(pm, s), G2(pm, s5, s4), R2(pm, s4, s7), R1(pm, s5, s4), Pre1(pm, s5), R1(pm, s2, S), R1(pm, s1, S), R1(pm, s1, s5), I(pm, s7) ⊦ ◇ last

User applied rule apply VD induction

And closed the goal!

Rule argument

subst: [R1, pm, R2, Pre1, s5, Post2, s, G2, s1, s2, I, G1, Post1, Pre2] → [R1, pm, R2, Pre1, s7, Post2, s, G2, s5, s4, I, G1, Post1, Pre2] path: 1, 1, 3, 1, 1, 3, 4, 6

Additional information

Used simplifier rules: l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: R1, pm, R2, Pre1, s7, Post2, s, G2, s5, s4, I, G1, Post1, Pre2