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Proof step 9 from proof onlymod-del (previous step)

rk0 ∈ st ↔ rk0 ∈ st0, rk ∈ st, ∀ rk. rk ∈ st ↔ rk ∈ st0, ∀ r0, sk. r0 ≠ r → st[r0 -- sk] = st0[r0 -- sk], r -- _type ∈ st → st[r -- _type] = st0[r -- _type], r -- _length ∈ st → st[r -- _length] = st0[r -- _length] ⊦ (r0 ≠ r → (st -- rk)[r0 -- sk] = (st0 -- rk)[r0 -- sk]) ∧ (r -- _type ≠ rk ∧ r -- _type ∈ st → st[r -- _type] = st0[r -- _type]) ∧ (r -- _length ≠ rk ∧ r -- _length ∈ st → st[r -- _length] = st0[r -- _length])

User applied rule all left

And obtained the following new goals

Proof step 8:
rk0 ∈ st ↔ rk0 ∈ st0, rk ∈ st, ∀ rk. rk ∈ st ↔ rk ∈ st0, r0 ≠ r → st[r0 -- sk] = st0[r0 -- sk], ∀ r0, sk. r0 ≠ r → st[r0 -- sk] = st0[r0 -- sk], r -- _type ∈ st → st[r -- _type] = st0[r -- _type], r -- _length ∈ st → st[r -- _length] = st0[r -- _length] ⊦ (r0 ≠ r → (st -- rk)[r0 -- sk] = (st0 -- rk)[r0 -- sk]) ∧ (r -- _type ≠ rk ∧ r -- _type ∈ st → st[r -- _type] = st0[r -- _type]) ∧ (r -- _length ≠ rk ∧ r -- _length ∈ st → st[r -- _length] = st0[r -- _length])

Rule argument

[EXRARG : pos: left 4, [extquanttermlist: (r0, sk)abort:F, discard:F, computed:F]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r0, sk)]]