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Proof step 81 from proof validrefs-put-notin-01 (previous step)

∀ r, fs, val, st, str, r0, ty. ¬ r ∈ acc ∧ fs ' ≠ _type ∧ fs ' ≠ _length ∧ oktype(val, fs .type, st) ∧ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) → (validrefs(str, acc + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, acc + r0 ', ty, st)) ⊦ ¬ r ∈ r1 + acc ∧ fs ' ≠ _type ∧ fs ' ≠ _length ∧ oktype(val, fs .type, st) ∧ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) → (validrefs(str, (r1 + acc) + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, (r1 + acc) + r0 ', ty, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
okval(val, fs .type), r -- fs ' ∈ st, okval(st[r -- fs '], fs .type), r ∈ st, ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ fs ' = _length, fs ' = _type, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, (r1 ' + acc) + r0 ', ty, st), r = r1, r ∈ acc

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]