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Proof step 124 from proof validval-put-any (previous step)

sk .fs = mkfs(class, ty, fieldvar), validval(str, r1 -- sk0, val, st), is_indexkey(sk), okval(refval(r0), st[r -- _type] .type .type), validref(str, r0, st[r -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk0 ⊦ validref(str, r0, st[r -- _type] .type .type, st[r1 -- sk0, val]), ( is_fskey(sk0) → (is_referencevalue(val) → validref(str, val .refval, sk0 .fs .type, st) ∧ is_reftype(sk0 .fs .type)) ∧ (¬ is_referencevalue(val) → okval(val, sk0 .fs .type) ∧ sk0 .fs .type ≠ void_type ∧ sk0 ≠ _length)) ∧ ( is_indexkey(sk0) → ( is_referencevalue(val) → validref(str, val .refval, st[r1 -- _type] .type .type, st) ∧ r1 ≠ jvmref ∧ is_arraytype(st[r1 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r1 -- _type] .type .type))) ∧ (¬ is_referencevalue(val) → okval(val, st[r1 -- _type] .type .type)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 123:
sk0 .fs = mkfs(class0, ty0, fieldvar0), sk .fs = mkfs(class, ty, fieldvar), validval(str, r1 -- sk0, val, st), is_indexkey(sk), okval(refval(r0), st[r -- _type] .type .type), validref(str, r0, st[r -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk0 ⊦ validref(str, r0, st[r -- _type] .type .type, st[r1 -- sk0, val]), ( is_fskey(sk0) → (is_referencevalue(val) → validref(str, val .refval, ty0, st) ∧ is_reftype(ty0)) ∧ (¬ is_referencevalue(val) → okval(val, ty0) ∧ ty0 ≠ void_type ∧ sk0 ≠ _length)) ∧ ( is_indexkey(sk0) → ( is_referencevalue(val) → validref(str, val .refval, st[r1 -- _type] .type .type, st) ∧ r1 ≠ jvmref ∧ is_arraytype(st[r1 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r1 -- _type] .type .type))) ∧ (¬ is_referencevalue(val) → okval(val, st[r1 -- _type] .type .type)))

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [sk0 .fs, class0, ty0, fieldvar0] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (sk0 .fs, class0, ty0, fieldvar0)]]