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Proof step 2 from proof valid-group-nodes-ls (previous step)

n < valid-group-nodes(gndx) ⊦ n < # gndx

User applied rule induction

And obtained the following new goals

Proof step 3:
φ([]) ∧ (∀ gndx, gnd. φ(gndx) → φ(gndx + gnd)) ⊦ φ(gndx)
Proof step 4:
⊦ (∀ n, gndx. [] = gndx ∧ n < valid-group-nodes(gndx) → n < # gndx) ∧ (∀ gndx, gnd. (∀ n, gndx1. gndx = gndx1 ∧ n < valid-group-nodes(gndx1) → n < # gndx1) → (∀ n, gndx1. gndx + gnd = gndx1 ∧ n < valid-group-nodes(gndx1) → n < # gndx1))

Rule argument

spec: <toplevel> name: induction-rev-list seq: φ([]) ∧ (∀ gndx, gnd. φ(gndx) → φ(gndx + gnd)) ⊦ φ(gndx) subst: [φ, gndx] → [λ gndx0. ∀ n, gndx. gndx0 = gndx ∧ n < valid-group-nodes(gndx) → n < # gndx, gndx]

Additional information

Used terms: λ gndx0. ∀ n, gndx. gndx0 = gndx ∧ n < valid-group-nodes(gndx) → n < # gndx, gndx