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Proof step 97 from proof hassharing-validrefs-dups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
path∃(str, r, r, st), validrefs(str, r ' + r1 ' + refs1, st[r -- _type] .type, st), ∀ st, str, refs, r0. # (r0 ' + refs) < # (r ' + (r1 + refs1)) → (validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = r1, hasSharing(r, st), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st), r ∈ refs1, ¬ r1 ∈ refs1 ∧ ¬ dups(refs1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ ¬ ¬ (r ∈ refs ∨ dups(refs))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]