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Proof step 16 from proof validrefs-maxlen (previous step)

fs = mkfs(class, ty1, fieldvar), is_obj(str, r, st), # st .refs ≤ # refs, st[r -- _type] .type ≤ ty, fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs ']), validrefs(str, st[r -- fs '] .refval ' + refs, ty1, st), ∀ str0, ty0, st0. validrefs(str0, st[r -- fs '] .refval ' + refs, ty0, st0) → # refs ≤ # st0 .refs ⊦ r = jvmref, r = st[r -- fs '] .refval, dups(refs), st[r -- fs '] .refval ∈ refs, r ∈ refs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
is_obj(str, r, st), # st .refs ≤ # refs, st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st), ∀ str0, ty0, st0. validrefs(str0, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty0, st0) → # refs ≤ # st0 .refs ⊦ r = jvmref, r = st[r -- mkfs(class, ty1, fieldvar) '] .refval, dups(refs), st[r -- mkfs(class, ty1, fieldvar) '] .refval ∈ refs, r ∈ refs

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]