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Proof step 29 from proof bint-is-cast (previous step)

32 < # int2bits(i) ⊦ ¬ 2147483647 < cast(32, i), bi2i(i2bi(cast(32, i))) = cast(32, i), i ∈bint

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
0 < cast(32, i), 32 < # int2bits(i), 2147483647 < cast(32, i) ⊦ bi2i(i2bi(cast(32, i))) = cast(32, i), i ∈bint

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)