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Proof step 10 from proof del-lists-1 (previous step)

⊦ _∃(λ x. (⌜n - # x = 0⌝ ∧ ls(r, x)) ∧ ⌜# x ≤ n⌝ ) = _∃(λ x. ls(r, x) ∧ ⌜n = # x⌝ ), r = null

User applied rule expand right

And obtained the following new goals

Proof step 11:
⊦ (_∃(λ x. (⌜n - # x = 0⌝ ∧ ls(r, x)) ∧ ⌜# x ≤ n⌝ ))(H) ↔ (_∃(λ x. ls(r, x) ∧ ⌜n = # x⌝ ))(H), r = null

Rule argument

pos: right 1

Additional information