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Theorem sis-pos-high

⊦ 0 ≤ i ∧ 32767 < i % 65536 → s2i(i2s(i)) = i % 65536 - 65536

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: short-in, short-larger, short-law-div-not, short-law-righthift-not, short-overflow, sis-ls-same, sis-neg-low, sis-pos-upper, ushort-pos-01, ushort-short,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 21
Proof steps: 33
Used lemmas: num-i2s-pos, num-issi,
Used spec theorems:
- int2bits/int2bits-mod2pot
- list-del/bitlista/lastN-rest-01
- list-del/bitlista/lastN-append
- list-data/bitlista/length-rest
- bitopsaux/fill-length
- bitopsaux/fillsgn-longer
- int2bits/int2int-rest
- int2bits/int2bits-pos
- int2bits/int2bits-len-pos
Used simplifier rules: