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Proof step 71 from proof validrefs-put-notin-01 (previous step)

r ∈ st, okval(st[r -- fs '], fs .type), r -- fs ' ∈ st, okval(val, fs .type), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ 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)) ⊦ r1 = jvmref, r = r1, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, (r1 ' + acc) + r0 ', ty, st), fs ' = _type, fs ' = _length, r ∈ acc

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 70:
fs = mkfs(class, ty1, fieldvar), r ∈ st, okval(st[r -- fs '], ty1), r -- fs ' ∈ st, okval(val, ty1), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ 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)) ⊦ r1 = jvmref, r = r1, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, (r1 ' + acc) + r0 ', ty, st), fs ' = _type, fs ' = _length, r ∈ acc

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class, ty1, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class, ty1, fieldvar)]]