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Proof step 39 from proof sis-neg-low (previous step)

16 = # int2bits(j0).rest, # int2bits(j0) = 17, i0 < 0, i0 * 65536 + j0 < 0, ~65536 < j0, i0 * 65536 + j0 < ~32768, j0 < ~32768, j0 < 0, j0 < ~1 ⊦ j0 = 0, int2bits(j0).rest = [], s2i(i2s(j0 + 65536)) = j0 + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i
Proof step 41:
¬(~32768 ≤ j0 + 65536 ∧ j0 + 65536 ≤ 32767), 16 = # int2bits(j0).rest, # int2bits(j0) = 17, i0 < 0, i0 * 65536 + j0 < 0, ~65536 < j0, i0 * 65536 + j0 < ~32768, j0 < ~32768, j0 < 0, j0 < ~1 ⊦ j0 = 0, int2bits(j0).rest = [], s2i(i2s(j0 + 65536)) = j0 + 65536

Rule argument

spec: inst: name: num-issi seq: ~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i subst: [i] → [j0 + 65536] flags: rewrite, current

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j0 + 65536