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Proof step 41 from proof hasSharing-dd-help (previous step)

# refs4 = # refs, # sks0 = 2 + # refs + # refs1, # refs1 = # refs2 + 1 + # refs0, fits(r, sks0, st), validrefs(str, r ' + refs + st[r -- firstn(1 + # refs, sks0)] .refval ' + refs1 + r0 ', st[r -- _type] .type, st), validrefs(str, r ' + refs4 + (st[r -- firstn(1 + # refs, sks0)] .refval ' + refs0) + r2 ' + refs2 + r0 ', st[r -- _type] .type, st), validrefs (str, (st[r -- firstn(1 + # refs, sks0)] .refval ' + refs0) + r2 ' + refs2 + r0 ', st[st[r -- firstn(1 + # refs, sks0)] .refval -- _type] .type, st) ⊦ r0 = jvmref, r2 = st[r -- firstn(1 + # refs, sks0)] .refval, st[r -- firstn(1 + # refs, sks0)] .refval = r0, hasSharing(r, st), path∃(str, r2, st[r -- firstn(1 + # refs, sks0)] .refval, st), path∃(str, st[r -- firstn(1 + # refs, sks0)] .refval, r2, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
st[r -- firstn(1 + # refs, sks0)] = refval(r1) ∧ is_referencevalue(st[r -- firstn(1 + # refs, sks0)]), # refs4 = # refs, # sks0 = 2 + # refs + # refs1, # refs1 = # refs2 + 1 + # refs0, fits(r, sks0, st), validrefs(str, r ' + refs + r1 ' + refs1 + r0 ', st[r -- _type] .type, st), validrefs(str, r ' + refs4 + (r1 ' + refs0) + r2 ' + refs2 + r0 ', st[r -- _type] .type, st), validrefs(str, (r1 ' + refs0) + r2 ' + refs2 + r0 ', st[r1 -- _type] .type, st) ⊦ r0 = jvmref, r2 = r1, r1 = r0, hasSharing(r, st), path∃(str, r2, r1, st), path∃(str, r1, r2, st)

Rule argument

[speclemmaarg: is_referencevalue(val) ,r = val .refval ↔ val = refval(r) ,[val, r] → [st[r -- firstn(1 + # refs, sks0)], r1] ,T ,javavalue , ,elim-refval ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_referencevalue(val) → val .refval = jvmref], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ validrefs (str, jvmref ' + refs, ty, st) ↔ refs = []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r -- firstn(1 + # refs, sks0)], r1)]]