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Proof step 35 from proof validrefs-put-notin-01 (previous step)

fs = mkfs(class0, ty2, fieldvar0), acc + r0 ' = st[r1 -- fs '] .refval ' + refs, st[r1 -- _type] .type ≤ ty, okval(val, ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r ∈ st, is_obj(str, r1, st), validrefs(str, acc + r0 ', ty2, st), is_referencevalue(st[r1 -- fs ']), fs ' ∈ instfields(st[r1 -- _type] .type .class), ∀ 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)) ⊦ r = r1, r1 = jvmref, mkfs(class, ty1, fieldvar) ' = _length, mkfs(class, ty1, fieldvar) ' = _type, r ∈ acc, ∃ fs0. fs0 ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs0 ']) ∧ st[r1 -- fs '] .refval = st[r1 -- fs0 '] .refval ∧ validrefs(str, st[r1 -- fs0 '] .refval ' + refs, fs0 .type, st[r -- mkfs(class, ty1, fieldvar) ', val]), r0 ≠ st[r1 -- fs '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- fs '] .refval ∈ acc ∧ st[r1 -- fs '] .refval ≠ r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
acc + r0 ' = st[r1 -- mkfs(class0, ty2, fieldvar0) '] .refval ' + refs, mkfs(class0, ty2, fieldvar0) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class0, ty2, fieldvar0) ']), validrefs(str, acc + r0 ', ty2, st), 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, r ∈ acc, ∃ fs0. fs0 ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs0 ']) ∧ st[r1 -- mkfs(class0, ty2, fieldvar0) '] .refval = st[r1 -- fs0 '] .refval ∧ validrefs(str, st[r1 -- fs0 '] .refval ' + refs, fs0 .type, st[r -- mkfs(class, ty1, fieldvar) ', val]), r0 ≠ st[r1 -- mkfs(class0, ty2, fieldvar0) '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- mkfs(class0, ty2, fieldvar0) '] .refval ∈ acc ∧ st[r1 -- mkfs(class0, ty2, fieldvar0) '] .refval ≠ r0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPFORWARD : ⊦ refs + r ' = refs0 → r ∈ refs0])]]