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Proof step 5 from proof nds-split (previous step)

nd ' + gndx0.nds = ndx0 + ndx1, gnd = mkgnode(nd, m, boolvar, boolvar0), ∀ ndx0, ndx1. gndx0.nds = ndx0 + ndx1 → (∃ gndx2, gndx1. gndx0 = gndx2 + gndx1 ∧ ndx0 = gndx2.nds ∧ ndx1 = gndx1.nds), nd ∈ ndx0 ∨ nd ∈ ndx1 ⊦ ∃ gndx, gndx1. gnd ' + gndx0 = gndx + gndx1 ∧ ndx0 = gndx.nds ∧ ndx1 = gndx1.nds

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
nd ' + gndx0.nds = ndx0 + ndx1, ∀ ndx0, ndx1. gndx0.nds = ndx0 + ndx1 → (∃ gndx2, gndx1. gndx0 = gndx2 + gndx1 ∧ ndx0 = gndx2.nds ∧ ndx1 = gndx1.nds), nd ∈ ndx0 ∨ nd ∈ ndx1 ⊦ ∃ gndx, gndx1. mkgnode(nd, m, boolvar, boolvar0) ' + gndx0 = gndx + gndx1 ∧ ndx0 = gndx.nds ∧ ndx1 = gndx1.nds

Rule argument

Additional information

Used simplifier rules: ⊦ nd ∈ ndx + ndx0 ↔ nd ∈ ndx ∨ nd ∈ ndx0; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]%in-14: ⊦ nd ' + ndx = ndx0 → nd ∈ ndx0; (forward) from specification list[node-list]