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Proof step 80 from proof validrefs-put-notin-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = [])
Proof step 78:
r1 ≠ jvmref, 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
Proof step 79:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []

Rule argument

[crewrite-arg: validrefs-null , F , [st, ty, refs, r, str] → [st[r -- fs ', val], ty, acc + r0 ', r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st[r -- fs ', val], ty, acc + r0 ', r1, str)]]