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Proof step 9 from proof spawn-rg-total-correct-strng (previous step)

□ (Rton(n)(S', S'') ∧ GInv(S) ∧ GInv(S')), ¬ GInv(S) ∨ n0 = N + 1 ∧ N = N'' + 1 until ¬ GInv(S''), INDHYP-nat0(n0), Rton(n)(s0, S), GInv(s), GInv(s0), boolvar → s = s0 ∧ n0 = n1 ⊦ ◇ last

User applied rule case distinction

And obtained the following new goals

Proof step 10:
□ (Rton(n)(S', S'') ∧ GInv(S) ∧ GInv(S')), INDHYP-nat0(n0), Rton(n)(s0, S), GInv(s), GInv(s0), boolvar → s = s0 ∧ n0 = n1, ¬ GInv(S) ⊦ ◇ last
Proof step 11:
□ (Rton(n)(S', S'') ∧ GInv(S) ∧ GInv(S')), N = N'' + 1 until ¬ GInv(S''), INDHYP-nat0(n0), Rton(n)(s0, S), GInv(s), GInv(s0), boolvar → s = s0 ∧ n0 = n1, n0 = N + 1 ⊦ ◇ last

Rule argument

pos: left 2

Proof step 9 from proof spawn-rg-total-correct-strng (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information