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Proof step 32 from proof validref-ac (previous step)

∀ str, r, ty, class, st. validref(str, r, ty, addclass(class, fis0, st)) ↔ validref(str, r, ty, st) ⊦ validref(str, r, ty, addclass(class, fv ' + fis0, st)) ↔ validref(str, r, ty, st)

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 23:
¬ (is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class), ∀ str, r, ty, class, st. validref(str, r, ty, addclass(class, fis0, st)) ↔ validref(str, r, ty, st) ⊦ validref(str, r, ty, addclass(class, fv ' + fis0, st)) ↔ validref(str, r, ty, st)
Proof step 31:
is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class, ∀ str, r, ty, class, st. validref(str, r, ty, addclass(class, fis0, st)) ↔ validref(str, r, ty, st) ⊦ validref(str, r, ty, addclass(class, fis0, st)) ↔ validref(str, r, ty, st)

Rule argument

[speclemmaarg: , is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class → addclass(class, fv ' + fis, st) = addclass(class, fis, st) ,[st, fis, fv, class] → [st, fis0, fv, class] ,F ,addfuns , ,ac-no1 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, fv, class)]]