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Proof step 1 from proof sis-neg-low (conclusion)

⊦ i < 0 ∧ i % 65536 < ~32768 → s2i(i2s(i)) = i % 65536 + 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i < 0, i % 65536 < ~32768 ⊦ s2i(i2s(i)) = i % 65536 + 65536, i % 65536 = 0

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%mod-ls-zero: 0 < j ⊦ i % (* j) < 0 ↔ i < 0 ∧ i % j ≠ 0; from specification int-div%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1