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Proof step 6 from proof mapex-put (previous step)

((r => o * P))(mk(rs, f)[r, o]), r ∈ rs ⊦ # rs = 0, rs = ∅, ((r => f(r) * P))(mk(rs, f)), ∃ o. ((r => o * P))(mk(rs, f))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ((r => o * P))(H) ↔ P(H -- r) ∧ r ∈ H ∧ H[r] = o
Proof step 8:
((r => o * P))(mk(rs, f)[r, o]), r ∈ rs ⊦ # rs = 0, rs = ∅, ∃ o. ((r => o * P))(mk(rs, f)), P(mk(rs, f) -- r) ∧ r ∈ mk(rs, f) ∧ mk(rs, f)[r] = f(r)

Rule argument

spec: maplet name: map-del seq: ⊦ ((r => o * P))(H) ↔ P(H -- r) ∧ r ∈ H ∧ H[r] = o subst: [H, P, o, r] → [mk(rs, f), P, f(r), r] flags: <all paths>

Additional information

Used terms: mk(rs, f), P, f(r), r