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Proof step 2 from proof modified-stays-reachable-rev (previous step)

reachable(r, r0, H[r0, ce]), r0 ∈ H ⊦ reachable(r, r0, H) ↔ true

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: modified-stays-reachable seq: ⊦ reachable(r, r0, H) → (reachable(r, r0, H[r0, ce]) ↔ true) subst: [r, r0, H, ce] → [r, r0, H[r0, ce], H[r0]]

Additional information

Used simplifier rules: ⊦ H[r, ce][r, ce0] = H[r, ce0]; (s)% ⊦ r ∈ H → H[r, H[r]] = H; (s) Used terms: r, r0, H[r0, ce], H[r0]