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Proof step 126 from proof setInt-theorem (previous step)

i >> 16 = b2i(i2b(i >> 16)), i >> 8 < ~128, i < ~128, i >> 8 < 0, i < 0 ⊦ i = b2i(i2b(i)), i2b(~1) = i2b(i >> 24)

User applied rule cut formula

And obtained the following new goals

Proof step 127:
b2i(i2b(i >> 16)) < 0, i >> 16 = b2i(i2b(i >> 16)), i >> 8 < ~128, i < ~128, i >> 8 < 0, i < 0 ⊦ i = b2i(i2b(i)), i2b(~1) = i2b(i >> 24)

Rule argument

fma: b2i(i2b(i >> 16)) < 0

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%shiftright-not-pos-01: ⊦ i < 0 → ¬ 0 ≤ i >> j; from specification intops Used formulas: b2i(i2b(i >> 16)) < 0