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Proof step 38 from proof validrefs-put-notin-01 (previous step)

acc + r0 ' = r4 ' + refs, is_obj(str, r1, st), r ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(val, ty1), 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)) ⊦ mkfs(class, ty1, fieldvar) ' = _type, mkfs(class, ty1, fieldvar) ' = _length, r1 = jvmref, r = r1, (∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r4 = st[r1 -- fs '] .refval ∧ validrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, st[r -- mkfs(class, ty1, fieldvar) ', val])) ↔ (∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r4 = st[r1 -- fs '] .refval ∧ validrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, st)), r ∈ acc, ¬ r4 ∈ acc ∧ r4 ≠ r0, r0 ≠ r4 ∧ ¬ r0 ∈ refs

User applied rule case distinction

And obtained the following new goals

Proof step 28:
∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r4 = st[r1 -- fs '] .refval ∧ validrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, st[r -- mkfs(class, ty1, fieldvar) ', val]), acc + r0 ' = r4 ' + refs, is_obj(str, r1, st), r ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(val, ty1), 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)) ⊦ ∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r4 = st[r1 -- fs '] .refval ∧ validrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, st), mkfs(class, ty1, fieldvar) ' = _type, mkfs(class, ty1, fieldvar) ' = _length, r1 = jvmref, r = r1, r ∈ acc, ¬ r4 ∈ acc ∧ r4 ≠ r0, r0 ≠ r4 ∧ ¬ r0 ∈ refs
Proof step 37:
∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r4 = st[r1 -- fs '] .refval ∧ validrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, st), acc + r0 ' = r4 ' + refs, is_obj(str, r1, st), r ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(val, ty1), 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)) ⊦ ∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r4 = st[r1 -- fs '] .refval ∧ validrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, st[r -- mkfs(class, ty1, fieldvar) ', val]), mkfs(class, ty1, fieldvar) ' = _type, mkfs(class, ty1, fieldvar) ' = _length, r1 = jvmref, r = r1, r ∈ acc, ¬ r4 ∈ acc ∧ r4 ≠ r0, r0 ≠ r4 ∧ ¬ r0 ∈ refs

Rule argument

[CASEDARG : pos: right 5, ()]

Additional information

[[CONCRETESIMPRULES : ()]]