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Proof step 8 from proof gfts-put (previous step)

∀ r, r0, st, sk0, val. r = r0 ∨ (goodfieldsandtypes(r, sks0, st[r0 -- sk0, val]) ↔ goodfieldsandtypes(r, sks0, st)) ⊦ r = r0, goodfieldsandtypes(r, sk + sks0, st[r0 -- sk0, val]) ↔ goodfieldsandtypes(r, sk + sks0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ goodfieldsandtypes(r, sk ' + sks, st) ↔ goodfieldandtype(r, sk, st) ∧ goodfieldsandtypes(r, sks, st)
Proof step 3:
⊦ goodfieldsandtypes(r, sk ' + sks, st) ↔ ¬ ¬ (goodfieldandtype(r, sk, st) ∧ goodfieldsandtypes(r, sks, st))
Proof step 7:
∀ r, r0, st, sk0, val. r = r0 ∨ (goodfieldsandtypes(r, sks0, st[r0 -- sk0, val]) ↔ goodfieldsandtypes(r, sks0, st)) ⊦ r = r0, goodfieldandtype(r, sk, st[r0 -- sk0, val]) ∧ goodfieldsandtypes(r, sks0, st[r0 -- sk0, val]) ↔ goodfieldandtype(r, sk, st) ∧ goodfieldsandtypes(r, sks0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ sk + sks = sk ' + sks])]]