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Proof step 6 from proof extensionality (previous step)

# x = # x0, ∀ n. n < # x0 → x[n] = x0[n] ⊦ x = x0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n])
Proof step 8:
# x = # x0, ∀ n. n < # x0 → x[n] = x0[n] ⊦ # x = # x0 ∧ (∀ n. n < # x → x[n] = x0[n])

Rule argument

spec: list-del inst: name: extension seq: ⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n]) subst: [y, x] → [x0, x] flags: rewrite

Additional information

Used terms: x0, x