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Proof step 13 from proof process-one (previous step)

H[r] = a × r0, ((del-list(r ' + rx0, n) * P))(H) ⊦ r0 = null, (1 ≤ n → ((del-list(r0 ' + rx0, n - 1) * P))(H -- r)) ∧ n ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ del-list(r ' + rx, n) = _∃(λ x. ls(r, x) * del-list(rx, n - # x) ∧ ⌜r ≠ null ∧ n ≥ # x⌝ )
Proof step 15:
H[r] = a × r0, ((_∃(λ x. ls(r, x) * del-list(rx0, n - # x) ∧ ⌜r ≠ null ∧ n ≥ # x⌝ ) * P))(H) ⊦ r0 = null, (1 ≤ n → ((del-list(r0 ' + rx0, n - 1) * P))(H -- r)) ∧ n ≠ 0

Rule argument

spec: del-lists 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, rx0, r] flags: <all paths>

Additional information

Used terms: n, rx0, r