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Proof step 7 from proof validfieldinits-rec (previous step)

sk0 .fs = mkfs(class0, ty0, fieldvar0), sk .fs = mkfs(class, ty, fieldvar), ∀ sk0, val0. sk0 × val0 = sk × val ∨ sk0 × val0 ∈ fis → is_fskey(sk0) ∧ okval(val0, sk0 .fs .type) ∧ ( is_referencevalue(val0) → val0 .refval = jvmref ∨ val0 .refval -- _type ∈ st ∧ is_typevalue(st[val0 .refval -- _type]) ∧ st[val0 .refval -- _type] .type ≤ sk0 .fs .type) ⊦ ¬ is_indexkey(sk) ∧ okval(val, ty) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty) ∧ ( sk0 × val0 ∈ fis → ¬ is_indexkey(sk0) ∧ okval(val0, ty0) ∧ ( is_referencevalue(val0) → val0 .refval = jvmref ∨ val0 .refval -- _type ∈ st ∧ is_typevalue(st[val0 .refval -- _type]) ∧ st[val0 .refval -- _type] .type ≤ ty0))

User applied rule all left

And obtained the following new goals

Proof step 6:
sk0 .fs = mkfs(class0, ty0, fieldvar0), sk .fs = mkfs(class, ty, fieldvar), sk × val = sk × val ∨ sk × val ∈ fis → is_fskey(sk) ∧ okval(val, sk .fs .type) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ sk .fs .type), ∀ sk0, val0. sk0 × val0 = sk × val ∨ sk0 × val0 ∈ fis → is_fskey(sk0) ∧ okval(val0, sk0 .fs .type) ∧ ( is_referencevalue(val0) → val0 .refval = jvmref ∨ val0 .refval -- _type ∈ st ∧ is_typevalue(st[val0 .refval -- _type]) ∧ st[val0 .refval -- _type] .type ≤ sk0 .fs .type) ⊦ ¬ is_indexkey(sk) ∧ okval(val, ty) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty) ∧ ( sk0 × val0 ∈ fis → ¬ is_indexkey(sk0) ∧ okval(val0, ty0) ∧ ( is_referencevalue(val0) → val0 .refval = jvmref ∨ val0 .refval -- _type ∈ st ∧ is_typevalue(st[val0 .refval -- _type]) ∧ st[val0 .refval -- _type] .type ≤ ty0))

Rule argument

[EXRARG : pos: left 3, [extquanttermlist: (sk, val)abort:F, discard:F, computed:T]]

Additional information

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