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Proof step 5 from proof hasKeys-put (previous step)

∀ r, r0, st, sk, val. r = r0 ∨ (hasKeys(r, sks0, st[r0 -- sk, val]) ↔ hasKeys(r, sks0, st)) ⊦ r = r0, r -- sk0 ∈ st ∧ hasKeys(r, sks0, st[r0 -- sk, val]) ↔ r -- sk0 ∈ st ∧ hasKeys(r, sks0, st)

User applied rule all left

And closed the goal!

Rule argument

[EXRARG : pos: left 1, [extquanttermlist: (r, r0, st, sk, val) abort:F , discard:T , computed:T ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, r0, st, sk, val)]]