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Theorem definedness-I12

⊦ ( (# gs.ar ≠ 0 ∧ htok(gs.ar)) ∧ allslotsfull(gs.ar, ls.n0, ls.n, ls.e, false) ∧ ls.n < # gs.ar ∧ ls.e ≠ ⊥ ∧ ls.sz = # gs.ar ∧ (ls.n0 < # gs.ar ∧ ls.n0 = get_hash(ls.e, ls.sz)) ∧ ¬ ls.b) ∧ pre(gs, ls, I12, a) → ls.n < # gs.ar ∧ (gs.ar[ls.n] = ⊥ ⊃ ls.n < # gs.ar;ls.n < # gs.ar)

Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by: HashsetInv-thm, other-HashsetLInv, rely-HashsetLInv, stable-HashsetLInv, step-HashsetLInv,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 2
Used lemmas:
Used spec theorems:
- Used simplifier rules:
  - Hashset/pre-I12
  - nat-basic/f