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Proof step 7 from proof hasSharing-pathex (previous step)

refs0 = [], refs1 + r0 ' = r1 ' + refs0, st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), is_obj(str, r, st), hasSharing(r0, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r1 ' + refs0, ty, st), ∀ st, r, str, refs. # refs < # (r1 ' + refs0) → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, hasSharing(r, st), r0 ≠ r1 ∧ ¬ r0 ∈ refs0, ¬ r1 ∈ refs1 ∧ r1 ≠ r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), validrefs(str, r0 ', ty, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), hasSharing(r0, st), is_obj(str, r, st), ∀ st, r, str, refs. # refs < # (r0 ' + []) → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, hasSharing(r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' = refs + r0 ' ↔ r = r0 ∧ refs = []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs])]]