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Proof step 53 from proof validfieldinits-def-01 (previous step)

∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ is_fskey(sk0) ∧ validval(str, val, sk0 .fs .type, st) ∧ type∃(str, sk0 .fs .type) ∧ validfieldinits(str, fis0, st) ↔ validfieldinits((sk0 × val) ' + fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 52:
sk0 .fs = mkfs(class, ty, fieldvar), ∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ is_fskey(sk0) ∧ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ validfieldinits(str, fis0, st) ↔ validfieldinits((sk0 × val) ' + fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [sk0 .fs, class, ty, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (sk0 .fs, class, ty, fieldvar)]]