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Proof step 3 from proof onlymod-length (previous step)

r -- _type ∈ st ↔ r -- _type ∈ st0, r -- _length ∈ st ↔ r -- _length ∈ st0, r -- _length ∈ st0 → st[r -- _length] = st0[r -- _length], r -- _type ∈ st0 → st[r -- _type] = st0[r -- _type], ∀ r0, sk. r0 ≠ r → st[r0 -- sk] = st0[r0 -- sk], ∀ rk. rk ∈ st ↔ rk ∈ st0 ⊦ st[r0 -- _length] = st0[r0 -- _length]

Heuristic quantifier applied rule all left

And obtained the following new goals

Rule argument

[EXRARG : pos: left 5, [QUANTTERMLIST : (r0, _length)]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]])], [EXTRATERMS : (r0, _length)]]