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Proof step 3 from proof map-putex-simp (conclusion)

r ∈ H ⊦ ¬ (r => o0 * P)(H[r, o1]) ↔ ¬ (o0 = o1 ∧ (r =>_ * P)(H))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
r ∈ H ⊦ ¬ (r => o0 * P)(H[r, o1]) ↔ o0 ≠ o1 ∨ ¬ (r =>_ * P)(H)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]