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Proof step 11 from proof sis-neg-high (previous step)

65536 = 2 ^ 16, # int2bits(j) ≤ 16, abs(j) < 65536, ~32768 ≤ j, i0 * 65536 + j < ~32768, j ≤ 0, i0 ≤ 0, i0 * 65536 + j < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 65536 + j))))) = j

User applied rule insert equation

And obtained the following new goals

Proof step 12:
# int2bits(j) ≤ 16, abs(j) < 2 ^ 16, ~32768 ≤ j, i0 * 2 ^ 16 + j < ~32768, j ≤ 0, i0 ≤ 0, i0 * 2 ^ 16 + j < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j))))) = j

Rule argument

pos: left 1 flags: discard

Proof step 11 from proof sis-neg-high (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information