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Proof step 7 from proof valid-eraseqd-rem-middle (previous step)

valid-eraseq(q + eqent ' + q1), ∀ eqent, q1. valid-eraseq(q + eqent ' + q1) → valid-eraseq(q + q1) ⊦ m ∈ q, m ∈ eqent ', m ∈ q1, ¬ m ∈ q + q1 ∧ valid-eraseq(q + q1)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
valid-eraseq(q + eqent ' + q1), valid-eraseq(q + q1), ∀ eqent, q1. valid-eraseq(q + eqent ' + q1) → valid-eraseq(q + q1) ⊦ m ∈ q1, m ∈ eqent ', m ∈ q, ¬ m ∈ q + q1 ∧ valid-eraseq(q + q1)
Proof step 11:
valid-eraseq(q + eqent ' + q1), ∀ eqent, q1. valid-eraseq(q + eqent ' + q1) → valid-eraseq(q + q1) ⊦ valid-eraseq(q + q1), m ∈ q1, m ∈ eqent ', m ∈ q, ¬ m ∈ q + q1 ∧ valid-eraseq(q + q1)

Rule argument

fma: valid-eraseq(q + q1)

Additional information

Used formulas: valid-eraseq(q + q1)