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Proof step 5 from proof map-putex (previous step)

((r => o1 * P))(H[r, o1]), ∃ H0, o. H = (H0 ++ r)[r, o] ∧ ¬ r ∈ H0 ⊦ r = null, ∃ o. ((r => o * P))(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
((r => o1 * P))((H0 ++ r)[r, o1]) ⊦ r = null, r ∈ H0, ∃ o0. ((r => o0 * P))((H0 ++ r)[r, o])

Rule argument

Additional information

Used simplifier rules: ⊦ H[r, o0][r, o1] = H[r, o1]; (s)