In the proof of the equivalence of SPI and WPI, it is said that SPI implies WPI and WPI implies SPI. But WPI and SPI are just proving techniques, what does it mean by one proving technique implying another. Is that 'WPI implies SPI' means that any statement proved by WPI could be proved by SPI?
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Yes, that and the assertion the other way is just what it means to say they are equivalent. – Ethan Bolker Dec 13 '21 at 18:47
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It means that with access to some standard set of techniques which does not include either form of induction, one can prove each instance of WPI from SPI and each instance of SPI from WPI. – Mark Saving Dec 13 '21 at 18:56