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Proof step 7 from proof okfieldinits-at (previous step)

okfieldinits(fs .class, 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) ⊦ ((fs ' × initial_value(fs .type)) ' + fis0)[mkfs(class, ty, fieldvar) '] = initial_value(ty), fs .type = abstract_type

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
fs = 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) ⊦ ((fs ' × initial_value(ty0)) ' + fis0)[mkfs(class, ty, fieldvar) '] = initial_value(ty), ty0 = abstract_type

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class1, ty0, fieldvar0] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class1, ty0, fieldvar0)]]