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Proof step 2 from proof zero-01 (previous step)

i < 0, j < 0 ⊦ i + j * (n→i(n) + 1) < 0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: nat2int-06: ⊦ ¬ n→i(n) + 1 < 0;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i < 0 → (0 < i * j ↔ j < 0); (s)% ⊦ i < i + j ↔ 0 < j; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%numlef-01: ⊦ (* i) ≤ j → i - 1 < j; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)