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Proof step 152 from proof validref-refs-last-valid-subset (previous step)

∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st), validref(str, r, st[r -- _type] .type, st), st ⊆ st0, r ∈ r0 + acc, validrefs(str, (r0 + acc) + r1 ', ty, st0) ⊦ validref(str, r1, st[r1 -- _type] .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 151:
validref(str, r, st[r -- _type] .type, st), st ⊆ st0, validrefs(str, (r0 ' + acc) + r1 ', ty, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc

Rule argument

[emptyarg]

Additional information

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