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Proof step 2 from proof sis-neg-low (previous step)

i < 0, i % 65536 < ~32768 ⊦ s2i(i2s(i)) = i % 65536 + 65536, i % 65536 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i
Proof step 4:
¬(~32768 ≤ i ∧ i ≤ 32767), i < 0, i % 65536 < ~32768 ⊦ s2i(i2s(i)) = i % 65536 + 65536, i % 65536 = 0

Rule argument

spec: byte inst: name: num-issi seq: ~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i subst: [i] → [i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%mod-ls-same-01: j ≠ 0 ⊦ i % j < i ↔ 0 < i ∧ (abs(j) = 1 ∨ abs(j) ≤ i); from specification int-div%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i