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Proof step 10 from proof ushort-short (previous step)

0 ≤ us2i(sho) ∧ 32767 < us2i(sho) % 65536, ¬(~32768 ≤ us2i(sho) ∧ us2i(sho) ≤ 32767) ⊦ us2i(sho) % 65536 - 65536 = s2i(sho)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: ushort-neg rotate: F subst: [sho] → [sho]

Additional information

Used simplifier rules: ushort-pos: ⊦ 0 ≤ s2i(sho) → us2i(sho) = s2i(sho);%short-mod: ⊦ s2i(sho) % 65536 = s2i(sho);%short-ngr: ⊦ ¬ 32767 < s2i(sho);% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i = i + j ↔ j = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; Used terms: sho