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Proof step 54 from proof spawn-sat-rg-strnger (previous step)

[:Inpf, S, Outf | [PL ¬ GInv(S) ∨ ¬ Pr(n0 + 1)(S)] ∥ [PL true]], GInv(s), m ≤ n0, ¬ Pr(m)(s), ∀ m0. m0 ≤ n0 + 1 → Pr(m0)(s) ⊦ Gton(n0 + 1)(s, s0) ∧ GInv(s0) ∧ ( Rton(n0 + 1)(s0, S) ∧ GInv(S) → (Rton(n0 + 1)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n0 + 1)(S) ∧ GInv(S);Gton(n0 + 1)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S'))))

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: m

Additional information

Used simplifier rules: lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; from specification nat-basic1%l-02: ⊦ ¬ m + n < m; 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: m