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Proof step 4 from proof valid-group-nodes-prefixn-append-nonend (previous step)

⊦ valid-group-nodes((n ≤ # gndx + 1 ⊃ firstn(n, gndx + mkgnode(nd, m, boolvar, false) ');gndx + mkgnode(nd, m, boolvar, false) ')) = valid-group-nodes(prefixn(n, gndx))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ prefixn(n, gndx) = (n ≤ # gndx ⊃ firstn(n, gndx);gndx)
Proof step 6:
⊦ valid-group-nodes((n ≤ # gndx + 1 ⊃ firstn(n, gndx + mkgnode(nd, m, boolvar, false) ');gndx + mkgnode(nd, m, boolvar, false) ')) = valid-group-nodes((n ≤ # gndx ⊃ firstn(n, gndx);gndx))

Rule argument

spec: list-prefixn, inst: group-store name: prefixn seq: ⊦ prefixn(n, gndx) = (n ≤ # gndx ⊃ firstn(n, gndx);gndx) subst: [gndx, n] → [gndx, n] flags: <all paths>

Additional information

Used terms: gndx, n