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Restrict substitution of arguments in quality to homotopy level 2 #302

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bvssvni opened this issue May 1, 2022 · 0 comments
Open

Restrict substitution of arguments in quality to homotopy level 2 #302

bvssvni opened this issue May 1, 2022 · 0 comments
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@bvssvni
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bvssvni commented May 1, 2022

Currently, quality::in_left_arg and quality::in_right_arg makes the following provable:

(a ~~ a) & (a == b) => (b ~~ b)

This is not provable in PSQ in Pocket-Prover, but one can prove the following:

(a ~~ a) & hom_eq(2, a, b) => (b ~~ b)

https://advancedresearch.github.io/quality/summary.html#psq---path-semantical-quantum-propositional-logic
hom_eq(2, a, b) == ((a == b) ⋀ (qubit(a) == qubit(b))) by Hom-2.
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