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Proof step 21 from proof fits-put-01 (previous step)

sk .fs = mkfs(class0, ty, fieldvar), st[r -- _type] .type = mkclasstype(class), st[r -- sk] = refval(r0), is_obj(str, r, st), okarray(r1, byte_type, st), fits(r0, sks0, st), r1 ∈ st, is_referencevalue(st[r0 -- sks0]), sk ∈ instfields(class), is_valid_ref(str, r0, st) → r0 = jvmref ∨ junkref(str, r0, st) ⊦ sks0 = [], r1 = jvmref, r = jvmref, r = r1, fits(r0, sks0, st[r1 -- i ', byteval(by)]), mkfs(class0, ty, fieldvar) ' ∈ instfields(class) ∧ is_referencevalue(st[r -- mkfs(class0, ty, fieldvar) ']) ∧ st[r -- mkfs(class0, ty, fieldvar) '] .refval ≠ jvmref ∧ (¬ st[st[r -- mkfs(class0, ty, fieldvar) '] .refval -- _type] .type ≤ ty ∨ junkref(str, st[r -- mkfs(class0, ty, fieldvar) '] .refval, st))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
sk .fs = mkfs(class0, ty, fieldvar), st[r -- _type] .type = mkclasstype(class), st[r -- sk] = refval(r0), is_obj(str, r, st), okarray(r1, byte_type, st), fits(r0, sks0, st), r1 ∈ st, is_referencevalue(st[r0 -- sks0]), sk ∈ instfields(class), is_valid_ref(str, r0, st) → r0 = jvmref ∨ junkref(str, r0, st) ⊦ is_fskey(sk), sks0 = [], r1 = jvmref, r = jvmref, r = r1, fits(r0, sks0, st[r1 -- i ', byteval(by)]), mkfs(class0, ty, fieldvar) ' ∈ instfields(class) ∧ is_referencevalue(st[r -- mkfs(class0, ty, fieldvar) ']) ∧ st[r -- mkfs(class0, ty, fieldvar) '] .refval ≠ jvmref ∧ (¬ st[st[r -- mkfs(class0, ty, fieldvar) '] .refval -- _type] .type ≤ ty ∨ junkref(str, st[r -- mkfs(class0, ty, fieldvar) '] .refval, st))
Proof step 20:
⊦ fits(jvmref, sks, st) ↔ sks = []

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) ∧ r ≠ jvmref → junkref(str, r, st)], [CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]