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Proof step 16 from proof bint-and-011x-bits2unit (previous step)

~2147483648 ≤ i, i < 0 ⊦ bits2int(fillsgn(32, int2bits(i))) + 2 ^ n→i(# fillsgn(32, int2bits(i))) = 4294967296 + i, fillsgn(32, int2bits(i)) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ i ∈bint → # fillsgn(32, int2bits(i)) = 32
Proof step 18:
i ∈bint, ~2147483648 ≤ i, i < 0 ⊦ bits2int(fillsgn(32, int2bits(i))) + 2 ^ n→i(32) = 4294967296 + i, fillsgn(32, int2bits(i)) = []

Rule argument

name: bint-fillsgn-len rotate: F subst: [i] → [i]

Additional information

Used simplifier rules: inbint: ⊦ i ∈bint ↔ ~2147483648 ≤ i ∧ i ≤ 2147483647;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; Used terms: i