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Proof step 7 from proof ushort-short (previous step)

¬(0 ≤ us2i(sho) ∧ 32767 < us2i(sho) % 65536), ¬(~32768 ≤ us2i(sho) ∧ us2i(sho) ≤ 32767) ⊦ s2i(i2s(us2i(sho))) = s2i(sho)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
us2i(sho) % 65536 < us2i(sho), 0 < us2i(sho), us2i(sho) % 65536 ≤ 32767, ~32768 ≤ us2i(sho), 32767 < us2i(sho) ⊦ i2s(us2i(sho)) = sho

Rule argument

Additional information

Used simplifier rules: short-equal: ⊦ s2i(shoi) = s2i(shoj) ↔ shoi = shoj;%ushort-nlsz: ⊦ ¬ us2i(sho) < 0;%i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;