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Theorem countrefs-lastn

⊦ # refs2 = i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)) ∧ lastn(i→n(countrefs(i1 ' + ints1)), r1 ' + refs2) = r0 ' + refs1 ∧ 0 ≤ i2 → ¬ # refs2 ≤ # refs1

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: multi-at-other, multi-field, multi-fieldin, multi-in-other, multi-isarrayref, multi-lengthin, multi-refin, multi-typein,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 5
Used lemmas: countrefs-not-zero-01,
Used spec theorems:
- list-data/references/length-neq
- list-del/references/lastN-length
Used simplifier rules:
- nat-basic2/l-02
- intnat/abs-zero
- nat-basic2/eq-01
- nat-basic1/f
- nat/lels-01
- list/references/len
- list/references/len-02
- nat-mult/rsucc-02
- nat-basic2/a
- nat-basic2/c
- nat-mult/mult-a
- nat-mult/mult-c
- nat/lep-02
- nat/anti
- nat-basic2/eq-inc-neq
- list/references/in-17
- list/references/in-append
- int-abs/forward-le-01
- list/references/a
- list/references/in-14