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Proof step 26 from proof validrefs-put-statfield (previous step)

is_obj(str, r, st[jvmref -- sk, val]) ∧ (st[jvmref -- sk, val][r -- _type]) .type ≤ ty, st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str, ty, st, sk, val. validrefs(str, acc, ty, st[jvmref -- sk, val]) ↔ validrefs(str, acc, ty, st) ⊦ acc = [] ∨ (∃ fs. fs ' ∈ instfields((st[jvmref -- sk, val][r -- _type]) .type .class) ∧ is_referencevalue(st[jvmref -- sk, val][r -- fs ']) ∧ acc .first = (st[jvmref -- sk, val][r -- fs ']) .refval ∧ validrefs(str, acc, fs .type, st[jvmref -- sk, val])) ↔ acc = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)), r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, ty, st, sk, val. validrefs(str, acc, ty, st[jvmref -- sk, val]) ↔ validrefs(str, acc, ty, st) ⊦ r = jvmref, (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st[jvmref -- sk, val])) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)), acc = []

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj (str, r, st[jvmref -- sk, val]) ↔ is_obj(str, r, st)], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]])]]