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Proof step 2 from proof sis-pos-high (previous step)

0 < i % 65536, 0 ≤ i, 32767 < i % 65536 ⊦ i % 65536 = s2i(i2s(i)) + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: byte inst: name: num-issi seq: ~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i subst: [i] → [i] flags: rewrite, current

Additional information

Used simplifier rules: numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%mod-ls-same-02: j ≠ 0 ⊦ i < i % j ↔ i < 0 ∧ (abs(j) = 1 ∨ abs(j) ≤ abs(i)); from specification int-div%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: i