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Proof step 141 from proof validrefs-put-notin-03 (previous step)

∀ str, r, st, sk, val, refs1, r0, ty. (is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val])) ∧ list2set(refs0) ∩ list2set(refs1) = ∅ → val .refval = r0 ∨ r0 = st[r -- sk] .refval ∨ sk = _type ∨ sk = _length ∨ (validrefs(str, refs0 + r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, refs0 + r ' + r0 ' + refs1, ty, st)) ∨ r = r0 ∨ dups(refs0) ∨ r0 ∈ refs0 ∨ r ∈ refs1 ∨ r ∈ refs0 ∨ dups(refs1) ∨ r0 ∈ refs1, is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]), list2set(r1 + refs0) ∩ list2set(refs1) = ∅ ⊦ val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, validrefs(str, (r1 + refs0) + r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, (r1 + refs0) + r ' + r0 ' + refs1, ty, st), r = r0, dups(r1 + refs0), r0 ∈ r1 + refs0, r ∈ refs1, r ∈ r1 + refs0, dups(refs1), r0 ∈ refs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 140:
is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]), list2set(refs1) ∩ list2set(refs0) = ∅, ∀ str0, r2, st0, sk0, val0, refs, r3, ty0. (is_valid_ref(str0, r2, st0) ↔ is_valid_ref(str0, r2, st0[r2 -- sk0, val0])) ∧ list2set(refs0) ∩ list2set(refs) = ∅ → val0 .refval = r3 ∨ r3 = st0[r2 -- sk0] .refval ∨ sk0 = _type ∨ sk0 = _length ∨ (validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0)) ∨ r2 = r3 ∨ r3 ∈ refs0 ∨ r2 ∈ refs ∨ r2 ∈ refs0 ∨ dups(refs) ∨ r3 ∈ refs ⊦ r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, validrefs(str, (r1 ' + refs0) + r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, (r1 ' + refs0) + r ' + r0 ' + refs1, ty, st), r0 = r1, r = r1, dups(refs1), r0 ∈ refs1, r1 ∈ refs1, dups(refs0), r1 ∈ refs0, r0 ∈ refs0, r ∈ refs1, r ∈ refs0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, in-06, ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPNAMEDSEQ : list-dup, references, dups-cons, ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPNAMEDSEQ : set-union, references, int-c, ⊦ rset ∩ rset0 = rset0 ∩ rset], [CSIMPNAMEDSEQ : set-union, references, int-a, ⊦ (rset ∩ rset0) ∩ rset1 = rset ∩ rset0 ∩ rset1], [CSIMPNAMEDSEQ : setlist, references, in, ⊦ r ∈ list2set(refs) ↔ r ∈ refs], [CSIMPNAMEDSEQ : set-union, references, int-ins, ⊦ rset ∩ (rset0 ++ r) = ∅ ↔ rset ∩ rset0 = ∅ ∧ ¬ r ∈ rset], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : setlist, references, list2set-rec, ⊦ list2set(r ' + refs) = list2set(refs) ++ r], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs])]]