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Proof step 1 from proof toar (conclusion)

⊦ ⌜ar⌝ .ar = ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ar = ar0 ↔ # ar = # ar0 ∧ (∀ n. n < # ar → ar[n] = ar0[n])
Proof step 3:
⊦ finp(⌜ar⌝ ) ↔ true
Proof step 4:
finp(σ) ⊦ # σ.ar = (# σ).n
Proof step 5:
⊦ # ⌜ar⌝ = ⌜# ar⌝
Proof step 6:
finp(σ), ⌜n⌝ < # σ ⊦ σ.ar[n] = σ[n]
Proof step 7:
⊦ n < # ar → ⌜ar⌝ [n] = ar[n]

Rule argument

spec: array, inst: dataarray name: Extension seq: ⊦ ar = ar0 ↔ # ar = # ar0 ∧ (∀ n. n < # ar → ar[n] = ar0[n]) subst: [ar0, ar] → [ar, ⌜ar⌝ .ar] flags: <all paths>

Additional information

Used simplifier rules: finp-ar: ⊦ finp(⌜ar⌝ ) ↔ true;%toar-size: finp(σ) ⊦ # σ.ar = (# σ).n;%tostream-size: ⊦ # ⌜ar⌝ = ⌜# ar⌝ ;%toar-at: finp(σ), ⌜n⌝ < # σ ⊦ σ.ar[n] = σ[n];%tostream-at: ⊦ n < # ar → ⌜ar⌝ [n] = ar[n];% ⊦ ⌜m⌝ .n = m; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s) Used terms: ar, ⌜ar⌝ .ar