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Proof step 7 from proof rm-vl-notin-before (previous step)

eq-entry(n, lref) ∈ (lref1 = lref0 ⊃ q0 - lref0;eq-entry(m, lref1) ' + (q0 - lref0)), ∀ n, lref, lref0. eq-entry(n, lref) ∈ q0 - lref0 → (∃ n. eq-entry(n, lref) ∈ q0) ⊦ ∃ n0. eq-entry(n0, lref) = eq-entry(m, lref1) ∨ eq-entry(n0, lref) ∈ q0

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
lref1 = lref0, eq-entry(n, lref) ∈ (lref1 = lref0 ⊃ q0 - lref0;eq-entry(m, lref1) ' + (q0 - lref0)), ∀ n, lref, lref0. eq-entry(n, lref) ∈ q0 - lref0 → (∃ n. eq-entry(n, lref) ∈ q0) ⊦ ∃ n0. eq-entry(n0, lref) = eq-entry(m, lref1) ∨ eq-entry(n0, lref) ∈ q0
Proof step 12:
eq-entry(n, lref) ∈ (lref1 = lref0 ⊃ q0 - lref0;eq-entry(m, lref1) ' + (q0 - lref0)), ∀ n, lref, lref0. eq-entry(n, lref) ∈ q0 - lref0 → (∃ n. eq-entry(n, lref) ∈ q0) ⊦ lref1 = lref0, ∃ n0. eq-entry(n0, lref) = eq-entry(m, lref1) ∨ eq-entry(n0, lref) ∈ q0

Rule argument

fma: lref1 = lref0

Additional information

Used formulas: lref1 = lref0