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Proof step 24 from proof addclass-switch (previous step)

is_fskey(sk), ∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ addclass(class, (sk × val0) ' + fis0, st[r -- i ', val]) = (addclass(class, (sk × val0) ' + fis0, st)[r -- i ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 16:
¬ (is_fskey((sk × val0) .1) ∧ (sk × val0) .1 .fs .class ≠ class), is_fskey(sk), ∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ addclass(class, (sk × val0) ' + fis0, st[r -- i ', val]) = (addclass(class, (sk × val0) ' + fis0, st)[r -- i ', val])
Proof step 23:
is_fskey((sk × val0) .1) ∧ (sk × val0) .1 .fs .class ≠ class, is_fskey(sk), ∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ addclass(class, fis0, st[r -- i ', val]) = (addclass(class, (sk × val0) ' + fis0, st)[r -- i ', val])

Rule argument

[crewrite-arg: ac-no1 , F , [st, fis, fv, class] → [st[r -- i ', val], fis0, sk × val0, class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- i ', val], fis0, sk × val0, class)]]