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Proof step 1 from proof tobuf (conclusion)

⊦ ⌜buf⌝ .buf = buf

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 3:
⊦ finp(⌜buf⌝ )
Proof step 4:
finp(σ) ⊦ # σ.buf = (# σ).n
Proof step 5:
⊦ # ⌜buf⌝ = ⌜# buf⌝
Proof step 6:
finp(σ), ⌜n⌝ < # σ ⊦ σ.buf[n] = σ[n]
Proof step 7:
⊦ n < # buf → ⌜buf⌝ [n] = buf[n]

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [buf, ⌜buf⌝ .buf] flags: <all paths>

Additional information

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