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Proof step 7 from proof del-lists-1 (previous step)

⊦ del-list(r ' + [], n) = _∃(λ x. ls(r, x) ∧ ⌜n = # x⌝ ), r = null

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ del-list(r ' + rx, n) = _∃(λ x. ls(r, x) * del-list(rx, n - # x) ∧ ⌜r ≠ null ∧ n ≥ # x⌝ )
Proof step 9:
⊦ _∃(λ x. ls(r, x) * del-list([], n - # x) ∧ ⌜r ≠ null ∧ n ≥ # x⌝ ) = _∃(λ x. ls(r, x) ∧ ⌜n = # x⌝ ), r = null

Rule argument

spec: <toplevel> name: del-list-rec seq: ⊦ del-list(r ' + rx, n) = _∃ (λ x. ls(r, x) * del-list(rx, n - # x) ∧ ⌜r ≠ null ∧ n ≥ # x⌝ ) subst: [n, rx, r] → [n, [], r] flags: <all paths>

Additional information

Used terms: n, [], r