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Proof step 55 from proof validrefs-putshort-field (previous step)

st[r0 -- mkfs(class0, ty0, fieldvar0) '] = refval(refs1 .first), mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, refs1, ty0, st[r0 -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_shortvalue(st[r0 -- mkfs(class, short_type, fieldvar) ']), is_obj(str, r0, st[r0 -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), st[r0 -- _type] .type ≤ ty, class0 ≠ class ∨ ty0 ≠ short_type ∨ fieldvar0 ≠ fieldvar, ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + refs1, ty, st), is_obj(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) ∧ oktype(val, fs .type, st) ∧ fs ' ≠ _type → (is_obj(str, r, st[r -- fs ', val]) ↔ is_obj(str, r, st)) ,[val, fs, st, r, str] → [shortval(sho), mkfs(class, short_type, fieldvar), st, r0, str] ,F ,addfuns , ,is_obj-put-samefield ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty], [CSIMPSEQ : ⊦ oktype(val, short_type, st) ↔ is_shortvalue(val)], [CSIMPSEQ : ⊦ is_shortvalue(shortval(sho))], [CSIMPSEQ : ⊦ mkfs (class1, short_type, fieldvar) ' ≠ _type], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ is_shortvalue(noval)])], [EXTRATERMS : (shortval(sho), mkfs(class, short_type, fieldvar), st, r0, str)]]