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Theorem gc-heap-fill-free-h

⊦ m ≤ n → gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m) = ∅

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: gc-heap-fill-free,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 7
Used lemmas: gc-heap-rec, gc-heap-base,
Used spec theorems:
- Used simplifier rules:
  - nat-basic/f
  - nat-basic/c
  - nat-basic/a
  - nat/succ-01
  - nat-basic/succ
  - nat/lels
  - nat/ls-le-simp
  - set-basic/gc-heap-rename-gc-heap-base-keyindex-set/size-zero-01
  - set-basic/gc-heap-rename-gc-heap-base-keyindex-set/size-zero
  - array/lp-array/Size-mkarray
  - array-copy/lp-array/size-fill
  - set-union/gc-heap-rename-gc-heap-base-keyindex-set/unc
  - set-union/gc-heap-rename-gc-heap-base-keyindex-set/una
  - set-union/gc-heap-rename-gc-heap-base-keyindex-set/une
  - lprops/disj-01
  - elem-index/gc-heap-base/sel-01-M03
  - array-copy/lp-array/at-fill-mkarray
  - nat/lels-03