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Proof step 11 from proof okfieldinits-at (previous step)

mkfs(class, ty, fieldvar) ' ∈ (sk × val) ' + fis0, okfieldinits(class0, (sk × val) ' + fis0), ∀ class, ty, fieldvar, class0. mkfs(class, ty, fieldvar) ' ∈ fis0 ∧ okfieldinits(class0, fis0) → fis0[mkfs(class, ty, fieldvar) '] = initial_value(ty) ⊦ ((sk × val) ' + fis0)[mkfs(class, ty, fieldvar) '] = initial_value(ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ okfieldinits(class, (sk × val) ' + fis) ↔ is_fskey(sk) ∧ val = initial_value(sk .fs .type) ∧ sk .fs .class = class ∧ sk .fs .type ≠ abstract_type ∧ okfieldinits(class, fis)
Proof step 10:
mkfs(class, ty, fieldvar) ' ∈ (sk × val) ' + fis0, is_fskey(sk) ∧ val = initial_value(sk .fs .type) ∧ sk .fs .class = class0 ∧ sk .fs .type ≠ abstract_type ∧ okfieldinits(class0, fis0), ∀ class, ty, fieldvar, class0. mkfs(class, ty, fieldvar) ' ∈ fis0 ∧ okfieldinits(class0, fis0) → fis0[mkfs(class, ty, fieldvar) '] = initial_value(ty) ⊦ ((sk × val) ' + fis0)[mkfs(class, ty, fieldvar) '] = initial_value(ty)

Rule argument

[crewrite-arg: okfieldinits-rec , F , [fis, val, sk, class] → [fis0, val, sk, class0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (fis0, val, sk, class0)]]