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Proof step 14 from proof onlymod-del (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ ¬ rk ∈ st ∧ onlyModified(r, st, st0) → ¬ rk ∈ st0
Proof step 13:
rk ∈ st, onlyModified(r, st, st0) ⊦ (rk0 ≠ rk ∧ rk0 ∈ st → rk0 ∈ st0) ∧ (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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ≠ rk0 → (st -- rk0)[rk] = st[rk]], [CSIMPSEQ : ⊦ rk ∈ st -- rk0 ↔ rk ≠ rk0 ∧ rk ∈ st])]]