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Proof step 20 from proof process-one (previous step)

((r => a0 × r0 * ls(r0, y) * del-list(rx0, n0) * P))(H) ⊦ r = null, r0 = null, ((del-list(r0 ' + rx0, n0 + # y) * P))(H -- r)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ del-list(r ' + rx, n) = _∃(λ x. ls(r, x) * del-list(rx, n - # x) ∧ ⌜r ≠ null ∧ n ≥ # x⌝ )
Proof step 22:
((r => a0 × r0 * ls(r0, y) * del-list(rx0, n0) * P))(H) ⊦ r = null, r0 = null, ((_∃(λ x. ls(r0, x) * del-list(rx0, n0 + # y - # x) ∧ ⌜r0 ≠ null ∧ n0 + # y ≥ # x⌝ ) * P))(H -- r)

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] → [n0 + # y, rx0, r0] flags: <all paths>

Additional information

Used terms: n0 + # y, rx0, r0