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Proof step 5 from proof induction-rev-list (previous step)

φ([]), ∀ gndx0, gnd. φ(gndx0) → φ(gndx0 + gnd '), ∀ gndx0, φ. # gndx0 < # gndx → φ([]) ∧ (∀ gndx0, gnd. φ(gndx0) → φ(gndx0 + gnd ')) → φ(gndx0) ⊦ gndx = [], φ(gndx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ gndx = [] ↔ ¬(∃ gndx0, gnd. gndx = gndx0 + gnd ')
Proof step 7:
φ([]), ∀ gndx0, gnd. φ(gndx0) → φ(gndx0 + gnd '), ∀ gndx0, φ. # gndx0 < # gndx → φ([]) ∧ (∀ gndx0, gnd. φ(gndx0) → φ(gndx0 + gnd ')) → φ(gndx0) ⊦ φ(gndx), ∀ gndx0, gnd. gndx ≠ gndx0 + gnd '

Rule argument

spec: list, inst: group-store name: lastdiv-rew seq: ⊦ gndx = [] ↔ ¬(∃ gndx0, gnd. gndx = gndx0 + gnd ') subst: [gndx] → [gndx] flags: <all paths>

Additional information

Used terms: gndx