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Proof step 13 from proof initial-value-01 (conclusion)

⊦ is_referencevalue(initial_value(ty)) ↔ is_reftype(ty) ∨ ty = void_type

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ initial_value(boolean_type) = boolval(false)
Proof step 2:
⊦ initial_value(int_type) = intval(0)
Proof step 3:
⊦ initial_value(short_type) = shortval(0s)
Proof step 4:
⊦ initial_value(byte_type) = byteval(0b)
Proof step 5:
⊦ initial_value(long_type) = longval(0l)
Proof step 6:
⊦ initial_value(float_type) = floatval(0f)
Proof step 7:
⊦ initial_value(double_type) = doubleval(0d)
Proof step 8:
⊦ initial_value(char_type) = charval(mkchar(0))
Proof step 9:
⊦ initial_value(void_type) = refval(jvmref)
Proof step 10:
⊦ initial_value(abstract_type) = noval
Proof step 11:
⊦ initial_value(mkclasstype(class1)) = refval(jvmref)
Proof step 12:
⊦ initial_value(mkarraytype(ty)) = refval(jvmref)

Rule argument

[VARWITHVARSEQSARG : ty, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : javatype generated by boolean_type, int_type, short_type, byte_type, long_type, float_type, double_type, char_type, void_type, abstract_type, mkclasstype, mkarraytype;], [CSIMPSEQ : ⊦ is_reftype(mkarraytype(ty))], [CSIMPSEQ : ⊦ is_reftype(mkclasstype(class))], [CSIMPSEQ : ⊦ void_type ≠ abstract_type], [CSIMPSEQ : ⊦ ¬ is_reftype(abstract_type)], [CSIMPSEQ : ⊦ ¬ is_referencevalue(noval)], [CSIMPSEQ : ⊦ ¬ is_reftype(void_type)], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ char_type ≠ void_type], [CSIMPSEQ : ⊦ ¬ is_reftype(char_type)], [CSIMPSEQ : ⊦ ¬ is_referencevalue(charval(jchar))], [CSIMPSEQ : ⊦ double_type ≠ void_type], [CSIMPSEQ : ⊦ ¬ is_reftype(double_type)], [CSIMPSEQ : ⊦ ¬ is_referencevalue (doubleval(doublevar))], [CSIMPSEQ : ⊦ float_type ≠ void_type], [CSIMPSEQ : ⊦ ¬ is_reftype(float_type)], [CSIMPSEQ : ⊦ ¬ is_referencevalue (floatval(floatvar))], [CSIMPSEQ : ⊦ long_type ≠ void_type], [CSIMPSEQ : ⊦ ¬ is_reftype(long_type)], [CSIMPSEQ : ⊦ ¬ is_referencevalue(longval(lo))], [CSIMPSEQ : ⊦ byte_type ≠ void_type], [CSIMPSEQ : ⊦ ¬ is_reftype(byte_type)], [CSIMPSEQ : ⊦ ¬ is_referencevalue(byteval(by))], [CSIMPSEQ : ⊦ short_type ≠ void_type], [CSIMPSEQ : ⊦ ¬ is_reftype(short_type)], [CSIMPSEQ : ⊦ ¬ is_referencevalue(shortval(sho))], [CSIMPSEQ : ⊦ boolean_type ≠ void_type], [CSIMPSEQ : ⊦ ¬ is_reftype(boolean_type)], [CSIMPSEQ : ⊦ ¬ is_referencevalue (boolval(boolvar))], [CSIMPSEQ : ⊦ ¬ is_referencevalue(intval(i))], [CSIMPSEQ : ⊦ ¬ is_reftype(int_type)], [CSIMPSEQ : ⊦ int_type ≠ void_type])]]