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One of the first big hurdles that mathematicians encounter when considering writing formal proofs is the necessity to get acquainted with the formal terminology and the parsing mechanisms used in the large ITP libraries. This includes the large number of formal symbols, the grammar of the formal languages and the advanced mechanisms instrumenting the proof assistants to correctly understand the formal expressions in the presence of ubiquitous overloading.

Abstract. Gaining insights into the evolution of Mediterranean Outflow Water (MOW) during the Early Pleistocene has been so far hampered by the lack of available palaeoclimatic archives. Here we present the first benthic foraminifera stable oxygen and carbon isotope records and grain-size data from IODP Expedition 339 Site U1389 presently located within the upper core of the MOW in the Gulf of Cadiz for the time interval between 2.6 and 1.8 Ma. A comparison with an intermediate water mass record from the Mediterranean Sea strongly suggest an active MOW supplying Site U1389 on glacial–interglacial timescales during the Early Pleistocene. We also find indication that the increasing presence of MOW in the Gulf of Cadiz during the investigated time interval aligns with the progressive northward protrusion of Mediterranean sourced intermediate water masses into the North Atlantic, possibly modulating the intensification of the North Atlantic Meridional Overturning Circulation at the same time. Additionally, our results suggest that MOW flow strength was already governed by precession and semi-precession cyclicity during the Early Pleistocene against the background of glacial–interglacial variability.

Gaining insights into the evolution of Mediterranean Outflow Water (MOW) during the Early Pleistocene climate transition has been so far hampered by the lack of available paleoclimatic archives. Here we present the first benthic foraminifera stable oxygen and carbon isotope records and grain-size data from IODP Expedition 339 Site U1389 presently located within the upper core of the MOW in the Gulf of Cadiz for the time interval between 2.6 and 1.8 Ma. A comparison with an intermediate water mass record from the Mediterranean Sea strongly suggest an active MOW supplying Site U1389 on glacial-interglacial timescales during the Early Pleistocene. We also find indication that the increasing presence of MOW in the Gulf of Cadiz during the investigated time interval aligns with the progressive northward protrusion of Mediterranean sourced intermediate water masses into the North Atlantic, possibly modulating the intensification of the North Atlantic Meridional Overturning Circulation at the same time. Additionally, our results suggest that MOW flow strength was already governed by precession and semi-precession cyclicity during the Early Pleistocene against the background of glacial-interglacial variability dominated by the obliquity cycle of Earth's inclination axis. Supplement to: Kaboth, Stefanie; Grunert, Patrick; Lourens, Lucas Joost (2017): Mediterranean Outflow Water variability during the Early Pleistocene. Climate of the Past, 13(8), 1023-1035