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Proof step 10 from proof hasSharing-pathex (previous step)

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), r0 ∈ refs0, r1 ∈ refs1, ∀ st, r, str, refs. # refs < # (r1 ' + refs0) → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st) ∧ hasSharing(refs0 .last, st), refs0 = [], r = jvmref, hasSharing(r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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), r0 ∈ refs0, r1 ∈ refs1, validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, 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)) ⊦ refs0 = [], r = jvmref, hasSharing(r, st), hasSharing(refs0 .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ validrefs (str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs (str, r ' + refs, ty, st)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]