Main-property⊦ ∀ x, dist.
calcDist-good(x) = dist
→ (∃ a_setOfActivity.
# a_setOfActivity ≥ 10000000 ∧ (∀ y. y ∈ a_setOfActivity → calcDist-good(y) = dist ∧ validGPSCoordinates(y))
∧ (∀ y, z. y ∈ a_setOfActivity ∧ z ∈ a_setOfActivity ∧ y ≠ z → mutuallyDisjointPositions(y, z)))distance-good-for-d-exactget-oneget-zerosize-defMain-property-aux3calcDist-good-properties
2071Main-property-proofMain-property-proof-info
The proof is valid.theorem
../../../../specs/filterDefs/export/unit.xmlfilterDefs../../../../specs/filterDefs/export/calcDist-good-def/longlemmainfo.xmlcalcDist-good-def../../../../../../lib/extended/specs/decimal/export/unit.xmldecimal../../../../../../lib/extended/specs/decimal/export/mkDecimal-enlarge/longlemmainfo.xmlmkDecimal-enlarge../../../../specs/filterDefs/export/unit.xmlfilterDefs../../../../specs/filterDefs/export/disjoint-set-def/longlemmainfo.xmldisjoint-set-def../../../../specs/filterDefs/export/unit.xmlfilterDefs../../../../specs/filterDefs/export/mutuallyDisjointPositions-def/longlemmainfo.xmlmutuallyDisjointPositions-def../../../../specs/filterDefs/export/unit.xmlfilterDefs../../../../specs/filterDefs/export/disjoint-activities-def/longlemmainfo.xmldisjoint-activities-def../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/forward-le-05/longlemmainfo.xmlforward-le-05../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/app/longlemmainfo.xmlapp../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/c/longlemmainfo.xmlc../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/lez/longlemmainfo.xmllez../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/ge/longlemmainfo.xmlge../../../../../../lib/basic/specs/set-basic/export/unit.xmlset-basicSetOfActivity../../../../../../lib/basic/specs/set-basic/export/size-zero/longlemmainfo.xmlsize-zero../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/zero-gels-04/longlemmainfo.xmlzero-gels-04../../../../specs/data-basic/export/unit.xmldata-basic../../../../specs/data-basic/export/elim-09/longlemmainfo.xmlelim-09../../../../specs/data-basic/export/unit.xmldata-basic../../../../specs/data-basic/export/sel-14/longlemmainfo.xmlsel-14../../../../../../lib/extended/specs/decimal-simple-ops/export/unit.xmldecimal-simple-ops../../../../../../lib/extended/specs/decimal-simple-ops/export/zero-def/longlemmainfo.xmlzero-def../../../../specs/data-basic/export/unit.xmldata-basic../../../../specs/data-basic/export/sel-13/longlemmainfo.xmlsel-13../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/len/longlemmainfo.xmllen../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/len-02/longlemmainfo.xmllen-02../../../../../../lib/basic/specs/nat-basic2/export/unit.xmlnat-basic2../../../../../../lib/basic/specs/nat-basic2/export/a/longlemmainfo.xmla../../../../../../lib/basic/specs/nat-basic2/export/unit.xmlnat-basic2../../../../../../lib/basic/specs/nat-basic2/export/c/longlemmainfo.xmlc../../../../../../lib/extended/specs/decimal-simple-ops/export/unit.xmldecimal-simple-ops../../../../../../lib/extended/specs/decimal-simple-ops/export/add-c/longlemmainfo.xmladd-c../../../../../../lib/extended/specs/decimal-simple-ops/export/unit.xmldecimal-simple-ops../../../../../../lib/extended/specs/decimal-simple-ops/export/add-a/longlemmainfo.xmladd-a../../../../../../lib/extended/specs/decimal-simple-ops/export/unit.xmldecimal-simple-ops../../../../../../lib/extended/specs/decimal-simple-ops/export/add-zero-01/longlemmainfo.xmladd-zero-01../../../../../../lib/basic/specs/nat-basic1/export/unit.xmlnat-basic1../../../../../../lib/basic/specs/nat-basic1/export/f/longlemmainfo.xmlf../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/let/longlemmainfo.xmllet../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/not-zero/longlemmainfo.xmlnot-zero../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/lels/longlemmainfo.xmllels../../../../../../lib/basic/specs/intnat/export/unit.xmlintnat../../../../../../lib/basic/specs/intnat/export/num-n2i-ls/longlemmainfo.xmlnum-n2i-ls../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/sub-ls/longlemmainfo.xmlsub-ls../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/minus-add/longlemmainfo.xmlminus-add../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/sub-ls-01/longlemmainfo.xmlsub-ls-01../../../../../../lib/extended/specs/decimal-simple-ops/export/unit.xmldecimal-simple-ops../../../../../../lib/extended/specs/decimal-simple-ops/export/less-same/longlemmainfo.xmlless-same../../../../../../lib/basic/specs/int-mult/export/unit.xmlint-mult../../../../../../lib/basic/specs/int-mult/export/associativity/longlemmainfo.xmlassociativity../../../../../../lib/basic/specs/int-mult/export/unit.xmlint-mult../../../../../../lib/basic/specs/int-mult/export/commutativity/longlemmainfo.xmlcommutativity../../../../../../lib/basic/specs/int-basic2/export/unit.xmlint-basic2../../../../../../lib/basic/specs/int-basic2/export/add-a/longlemmainfo.xmladd-a../../../../../../lib/basic/specs/int-basic2/export/unit.xmlint-basic2../../../../../../lib/basic/specs/int-basic2/export/add-c/longlemmainfo.xmladd-c../../../../../../lib/extended/specs/decimal-simple-ops/export/unit.xmldecimal-simple-ops../../../../../../lib/extended/specs/decimal-simple-ops/export/le-same/longlemmainfo.xmlle-same../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/sub-le/longlemmainfo.xmlsub-le../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/numle-02/longlemmainfo.xmlnumle-02../../../../../../lib/basic/specs/intnat/export/unit.xmlintnat../../../../../../lib/basic/specs/intnat/export/num-n2i-ls-07/longlemmainfo.xmlnum-n2i-ls-07../../../../../../lib/basic/specs/oelem/export/unit.xmloelemintlista../../../../../../lib/basic/specs/oelem/export/lel/longlemmainfo.xmllel../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/in-14/longlemmainfo.xmlin-14../../../../specs/data-basic/export/unit.xmldata-basic../../../../specs/data-basic/export/elim-08/longlemmainfo.xmlelim-08../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/in-17/longlemmainfo.xmlin-17../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/in-append/longlemmainfo.xmlin-append../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/forward-le-01/longlemmainfo.xmlforward-le-01../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/a/longlemmainfo.xmla../../../../../../lib/basic/specs/list/export/unit.xmllistlistOfGPSPos../../../../../../lib/basic/specs/list/export/in-15/longlemmainfo.xmlin-15../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/elim-sub/longlemmainfo.xmlelim-sub../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/ge-def/longlemmainfo.xmlge-def../../../../../../lib/basic/specs/int-abs/export/unit.xmlint-abs../../../../../../lib/basic/specs/int-abs/export/numlelsdel/longlemmainfo.xmlnumlelsdel../../../../specs/data-lib-funs/export/unit.xmldata-lib-funs../../../../specs/data-lib-funs/export/round-Math-def/longlemmainfo.xmlround-Math-def