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a proof language (embedded in nial)
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| r0 := ("^^>^* (ph 'exponent rule') | |
| (("$x "^ "$y) "^ "$z) | |
| "= (("$x "^ ("$y "* "$z)))) | |
| r1 := ("xy>yx (ph 'commutative rule for *') | |
| ("x "* "y) | |
| "= ("y "* "x)) | |
| p := (("x "^ "y) "^ "z); | |
| q := (("x "^ "z) "^ "y); | |
| t := { show p "= q ( | |
| (("x "^ "y) "^ "z) "| "r0 | |
| "= ("x "^ ("y "* "z)) "| "r1 | |
| "= ("x "^ ("z "* "y)) "| "_r | |
| "= (("x "^ "z) "^ "y) ) } |
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