prolong a linepromissory noteproofproof and refutationproof by accuracyproof by casesproof by contradictionproof by descentproof by exhibiting a modelproof by inductionproof by interpretationproof by reduction ad absurdumproof of accuracyproof of existenceproof of uniquenessproof theorypropagatepropagationpropagation of errorpropagation of errorspropagation velocitypropayationproperproper amountproper classproper conicproper directionproper disjunctive propositionproper divisor of zeroproper faceproper factorproper fractionproper frequencyproper inclusionproper quadric surfaceproper rational functionproper setproper subclassproper subgroupproper subsetproper time intervalproper transformproper valueproper vectorproperlyproperly contained inproperly discontinuous transformation groupproperly divergentproperly divergent sequenceproperly divergent series