Clumsy existential

this might be a stupid suspicions about: i often want to prove something like this:(∃ v . e → v) ↔ (∃ v′ ~ v . [[e]] → v′)except that the span doesn’t work loophole: v is only in scope in the first parenthesized proposition, so it can’t be referred to in the second one. of tack, it’s generally sufficient to prove co-termination and barely leave out the relationship between the final values, since that’s regularly indubitably derivable. but it’s an important part of the intuition behind correctness, so i want the relationship between answers to be in the communication of the theorem.an awkward character to make this work is to write big clunky conjunctions like:(e↓ ↔ [[e]]↓) ∧ (∀ v . e → v . ∃ v′ ~ v . [[e]] → v′)but it would be gracious if there were some way to send a letter it more compactly like the first pseudo-proposition i wrote. i like that it reads almost like you’d aver in english: “e and [[e]] always hit it off with b manage the same answers.”anyone have any suggestions?

Hunter parrish

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