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Proof step 5 from proof switch-class-01 (previous step)

∀ r, i, class, fis, st. addarray(r, vals0, i, addclass(class, fis, st)) = addclass(class, fis, addarray(r, vals0, i, st)) ⊦ (addarray(r, vals0, i + 1, addclass(class, fis, st))[r -- i ', val]) = addclass(class, fis, addarray(r, vals0, i + 1, st)[r -- i ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ addclass(class, fis, st[r -- i ', val]) = (addclass(class, fis, st)[r -- i ', val])
Proof step 4:
∀ r, i, class, fis, st. addarray(r, vals0, i, addclass(class, fis, st)) = addclass(class, fis, addarray(r, vals0, i, st)) ⊦ (addarray(r, vals0, i + 1, addclass(class, fis, st))[r -- i ', val]) = (addclass(class, fis, addarray(r, vals0, i + 1, st))[r -- i ', val])

Rule argument

[speclemmaarg: , addclass(class, fis, st[r -- i ', val]) = (addclass(class, fis, st)[r -- i ', val]) ,[val, i, r, st, fis, class] → [val, i, r, addarray(r, vals0, i + 1, st), fis, class] ,F ,addfuns , ,addclass-switch ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, i, r, addarray(r, vals0, i + 1, st), fis, class)]]