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Proof step 82 from proof validrefs-putshort-field (previous step)

is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), is_obj(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), st[r0 -- _type] .type ≤ ty, refs1 = [] ∨ mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- mkfs(class0, ty0, fieldvar0) ']) ∧ refs1 .first = (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- mkfs(class0, ty0, fieldvar0) ']) .refval ∧ validrefs(str, refs1, ty0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 -- mkfs(class0, ty0, fieldvar0) ' = r -- mkfs(class, short_type, fieldvar) ', r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + refs1, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), is_obj(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), st[r0 -- _type] .type ≤ ty, refs1 = [] ∨ mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- mkfs(class0, ty0, fieldvar0) ']) ∧ refs1 .first = (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- mkfs(class0, ty0, fieldvar0) ']) .refval ∧ validrefs(str, refs1, ty0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), r0 ≠ r ∨ class0 ≠ class ∨ ty0 ≠ short_type ∨ fieldvar0 ≠ fieldvar, ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + refs1, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]