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Proof step 11 from proof gfts-all (previous step)

∀ r, st. (∀ sk. sk ∈ sks0 → goodfieldandtype(r, sk, st)) → goodfieldsandtypes(r, sks0, st), ∀ sk0. sk0 ∈ sk + sks0 → goodfieldandtype(r, sk0, st) ⊦ goodfieldsandtypes(r, sk + sks0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ goodfieldsandtypes(r, sk ' + sks, st) ↔ ¬ ¬ (goodfieldandtype(r, sk, st) ∧ goodfieldsandtypes(r, sks, st))
Proof step 10:
∀ r, st. (∀ sk. sk ∈ sks0 → goodfieldandtype(r, sk, st)) → goodfieldsandtypes(r, sks0, st), ¬ goodfieldandtype(r, sk, st) ∨ ¬ goodfieldsandtypes(r, sks0, st), ∀ sk0. sk0 = sk ∨ sk0 ∈ sks0 → goodfieldandtype(r, sk0, st) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ sk ∈ sk0 ' + sks ↔ sk ≠ sk0 ∧ ¬ sk ∈ sks], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ sk + sks = sk ' + sks])]]