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Proof step 103 from proof validrefs-not-contains (previous step)

validrefs(str, st[r -- fs '] .refval ' + refs0 + r1 ', fs .type, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str0, st0, ty0. ¬ contains(str0, st0[st[r -- fs '] .refval -- _type] .type, st0[r1 -- _type] .type) ∧ st[r -- fs '] .refval ≠ r1 → ¬ validrefs(str0, st[r -- fs '] .refval ' + refs0 + r1 ', ty0, st0) ⊦ r = jvmref, r = r1, r1 = jvmref, contains(str, st[r -- _type] .type, st[r1 -- _type] .type)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 102:
fs = mkfs(class, ty1, fieldvar), validrefs(str, st[r -- fs '] .refval ' + refs0 + r1 ', ty1, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str0, st0, ty0. ¬ contains(str0, st0[st[r -- fs '] .refval -- _type] .type, st0[r1 -- _type] .type) ∧ st[r -- fs '] .refval ≠ r1 → ¬ validrefs(str0, st[r -- fs '] .refval ' + refs0 + r1 ', ty0, st0) ⊦ r = jvmref, r = r1, r1 = jvmref, contains(str, st[r -- _type] .type, st[r1 -- _type] .type)

Rule argument

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

Additional information

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