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Proof step 2 from proof mapex-new-rw (previous step)

⊦ r = null, ¬ (r =>_ * P)(H ++ r) ↔ ¬ P(H), r ∈ H

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
¬ r ∈ H, r ≠ null ⊦ P(H) ↔ (r =>_ * P)(H ++ r)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: mapex-new antecedent: ¬ r ∈ H, r ≠ null succedent: P(H) ↔ (r =>_ * P)(H ++ r) substlist: [r, H, P] → [r, H, P] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, H, P)]]