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Proof step 18 from proof long-is-cast (previous step)

¬ 0 < i, # int2bits(i) ≤ 64 ⊦ l2i(i2l(bits2int(lastn(64, int2bits(i))))) = cast(64, i), ¬ i < ~9223372036854775808 ∧ ¬ 9223372036854775807 < i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
i < 0, i < ~9223372036854775808, # int2bits(i) ≤ 64 ⊦ l2i(i2l(bits2int(lastn(64, int2bits(i))))) = cast(64, i)

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;