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Proof step 6 from proof mk-exists (previous step)

∀ H0. # H0 < # H → true → (∃ rs, f. H0 = mk(rs, f)) ⊦ H = ∅, ∃ rs, f. H = mk(rs, f)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 8:
∀ H0. # H0 < # H → true → (∃ rs, f. H0 = mk(rs, f)) ⊦ ∀ r. (r ∈ H ↔ r ∈ ∅) ∧ (r ∈ H → H[r] = (∅)[r]), ∃ rs, f. H = mk(rs, f)

Rule argument

spec: heap name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [∅, H] flags: <all paths>

Additional information

Used terms: ∅, H