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Proof step 6 from proof dec2int-not-neg (previous step)

¬(0 ≤ dec.int ∧ 0 < 10 ^ dec.scale), mkDecimal(0, 0) ≤ dec, dec.int / 10 ^ dec.scale < 0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
mkDecimal(0, 0) ≤ dec, dec.int / 10 ^ dec.scale < 0, 0 < 10 ^ dec.scale, dec.int < 0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%scale-not-neg: ⊦ ¬ dec.scale < 0; from specification decimal%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%grz: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j); from specification int-pot