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Proof step 25 from proof process-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ((r => ce * P))(H) ↔ P(H -- r) ∧ r ∈ H ∧ H[r] = ce

Rule argument

spec: maplet, inst: cell-heap name: map-del seq: ⊦ ((r => ce * P))(H) ↔ P(H -- r) ∧ r ∈ H ∧ H[r] = ce subst: [H, P, ce, r] → [H, ls(r0, y) * del-list(rx0, n0) * P, a0 × r0, r] flags: <all paths>

Additional information

Used simplifier rules: sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep Used terms: H, ls(r0, y) * del-list(rx0, n0) * P, a0 × r0, r