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Proof step 7 from proof tostream-inj (previous step)

# ar0 = # ar1, ∀ n. n < # ar1 → ar0[n] = ar1[n] ⊦ ar0 = ar1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ar = ar0 ↔ # ar = # ar0 ∧ (∀ n. n < # ar → ar[n] = ar0[n])
Proof step 9:
# ar0 = # ar1, ∀ n. n < # ar1 → ar0[n] = ar1[n] ⊦ # ar0 = # ar1 ∧ (∀ n. n < # ar0 → ar0[n] = ar1[n])

Rule argument

spec: array, inst: dataarray name: Extension seq: ⊦ ar = ar0 ↔ # ar = # ar0 ∧ (∀ n. n < # ar → ar[n] = ar0[n]) subst: [ar0, ar] → [ar1, ar0] flags: <all paths>

Additional information

Used terms: ar1, ar0