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Proof step 5 from proof okfieldinits-at (previous step)

okfieldinits(class1, fis0), mkfs(class, ty, fieldvar) ' ∈ fis0, ∀ class, ty, fieldvar, class0. mkfs(class, ty, fieldvar) ' ∈ fis0 ∧ okfieldinits(class0, fis0) → fis0[mkfs(class, ty, fieldvar) '] = initial_value(ty) ⊦ ((mkfs(class1, ty0, fieldvar0) ' × initial_value(ty0)) ' + fis0)[mkfs(class, ty, fieldvar) '] = initial_value(ty), ty0 = abstract_type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ sk ≠ sk0 → ((sk0 × val) ' + fis)[sk] = fis[sk]
Proof step 4:
mkfs(class, ty, fieldvar) ' ≠ mkfs(class1, ty0, fieldvar0) ', okfieldinits(class1, fis0), mkfs(class, ty, fieldvar) ' ∈ fis0, ∀ class, ty, fieldvar, class0. mkfs(class, ty, fieldvar) ' ∈ fis0 ∧ okfieldinits(class0, fis0) → fis0[mkfs(class, ty, fieldvar) '] = initial_value(ty) ⊦ fis0[mkfs(class, ty, fieldvar) '] = initial_value(ty), ty0 = abstract_type

Rule argument

[speclemmaarg: ,sk ≠ sk0 → ((sk0 × val) ' + fis)[sk] = fis[sk] ,[sk, fis, val, sk0] → [mkfs(class, ty, fieldvar) ', fis0, initial_value(ty0), mkfs(class1, ty0, fieldvar0) '] ,F ,assoclist ,fieldinit ,assoc-no ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ ((sk × val) ' + fis)[sk] = val], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])], [EXTRATERMS : (mkfs(class, ty, fieldvar) ', fis0, initial_value(ty0), mkfs(class1, ty0, fieldvar0) ')]]