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Proof step 28 from proof validrefs-put-notin-02 (previous step)

acc + r0 ' = st[r1 -- fs '] .refval ' + refs, validrefs(str, acc + r0 ', fs .type, st), is_referencevalue(st[r1 -- fs ']), fs ' ∈ instfields(st[r1 -- _type] .type .class), okval(val, ty0), is_obj(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r = r1, r1 = jvmref, r ∈ acc, r0 ≠ st[r1 -- fs '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- fs '] .refval ∈ acc ∧ st[r1 -- fs '] .refval ≠ r0, ∃ fs0. fs0 ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs0 ']) ∧ (acc + r0 ') .first = st[r1 -- fs0 '] .refval ∧ validrefs(str, acc + r0 ', fs0 .type, st[r -- mkfs(class, ty0, fieldvar) ', val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 27:
fs = mkfs(class0, ty1, fieldvar0), acc + r0 ' = st[r1 -- fs '] .refval ' + refs, validrefs(str, acc + r0 ', ty1, st), is_referencevalue(st[r1 -- fs ']), fs ' ∈ instfields(st[r1 -- _type] .type .class), okval(val, ty0), is_obj(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r = r1, r1 = jvmref, r ∈ acc, r0 ≠ st[r1 -- fs '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- fs '] .refval ∈ acc ∧ st[r1 -- fs '] .refval ≠ r0, ∃ fs0. fs0 ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs0 ']) ∧ (acc + r0 ') .first = st[r1 -- fs0 '] .refval ∧ validrefs(str, acc + r0 ', fs0 .type, st[r -- mkfs(class, ty0, fieldvar) ', val])

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class0, ty1, fieldvar0] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class0, ty1, fieldvar0)]]