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Proof step 143 from proof hasSharing-dd-help (previous step)

refs1 = refs2 + r0 ', r1 ' + refs0 = refs + r0 ', path∃(str, r, r2, st), path∃(str, r, r1, st), validrefs(str, r2 ' + refs1, st[r2 -- _type] .type, st), validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st) ⊦ refs1 = [], r2 = r1, r0 = jvmref, hasSharing(r, st), path∃(str, r1, r2, st), path∃(str, r2, r1, st), ¬ r1 ∈ refs ∧ r1 ≠ r0, r0 ≠ r1 ∧ ¬ r0 ∈ refs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 142:
r1 ' + refs0 = refs + refs0 .last ', r1 ∈ refs, path∃(str, r, r2, st), path∃(str, r, r1, st), validrefs(str, r2 ' + refs2 + refs0 .last ', st[r2 -- _type] .type, st), validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st) ⊦ refs0 = [], r2 = r1, refs0 .last = jvmref, r1 = refs0 .last, hasSharing(r, st), path∃(str, r1, r2, st), path∃(str, r2, r1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPSEQ : ⊦ r ∈ refs → r ∈ refs + refs0], [CSIMPSEQ : ⊦ refs .last ∈ refs ↔ refs ≠ []], [CSIMPFORWARD : ⊦ refs + r ' = refs0 → r ∈ refs0], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0], [CSIMPFORWARD : ⊦ r ' + refs = refs0 + r0 ' ∧ r ≠ r0 → r ∈ refs0 ∧ r0 ∈ refs], [CSIMPFORWARD : ⊦ r ' + refs = refs0 + r0 ' ∧ r ≠ r0 → refs .last = r0], [CSIMPSEQ : ⊦ ¬ path∃(str, r, r0, st) → ¬ validrefs (str, r ' + refs + r0 ', ty, st)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + r ' ≠ []])]]