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Proof step 8 from proof valid-eraseqd-append (previous step)

∀ m, lref. valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ q0 ∧ valid-eraseq(q0) ⊦ ¬ m0 ∈ q0 + eq-entry(m, lref) ' ∧ valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ eq-entry(m0, lref0) ' + q0 ∧ ¬ m0 ∈ q0 ∧ valid-eraseq(q0)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 9:
valid-eraseq(q0), ∀ m, lref. valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ q0 ∧ valid-eraseq(q0) ⊦ ¬ m0 ∈ q0 + eq-entry(m, lref) ' ∧ valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ eq-entry(m0, lref0) ' + q0 ∧ ¬ m0 ∈ q0 ∧ valid-eraseq(q0)
Proof step 15:
∀ m, lref. valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ q0 ∧ valid-eraseq(q0) ⊦ ¬ m0 ∈ q0 + eq-entry(m, lref) ' ∧ valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ eq-entry(m0, lref0) ' + q0 ∧ ¬ m0 ∈ q0 ∧ valid-eraseq(q0), valid-eraseq(q0)

Rule argument

fma: valid-eraseq(q0)

Additional information

Used formulas: valid-eraseq(q0)